FILTER ARRAY AND LIGHT DETECTION SYSTEM

Abstract

A filter array used in a light detection device, which generates image data corresponding to each of N wavelength bands (N being an integer greater than or equal to 2) included in a specific wavelength range, includes optical filters. The optical filters include various types of optical filters with different light transmittance with respect to each wavelength band. Mi≥0.1 with respect to each wavelength band, where Mi=μi−σi, μi denoting an average value of light transmittance of the optical filters with respect to light having a wavelength included in an i-th wavelength band (i being an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, σi denoting a standard deviation of the light transmittance of the optical filters with respect to the light having the wavelength included in the i-th wavelength band.

Description

BACKGROUND

1. Technical Field

The present disclosure relates to filter arrays and light detection systems.

2. Description of the Related Art

By utilizing spectral information about a large number of bands, such as several tens of bands, each being a narrow band, detailed characteristics of a target object can be ascertained, which is not possible with a conventional RGB image. A camera that acquires such multi-wavelength information is called a “hyperspectral camera”. Hyperspectral cameras are used in various fields, such as in food inspection, biological examination, drug development, and mineral component analysis.

U.S. Pat. No. 9,599,511 discloses an example of a hyperspectral imaging device that utilizes compressed sensing. This imaging device includes an encoder as an array of optical filters with different wavelength dependency with respect to light transmittance, an image sensor that detects light transmitted through the encoder, and a signal processing circuit. The encoder is disposed on an optical path that connects a subject and the image sensor. For each pixel, the image sensor simultaneously detects light on which components of wavelength bands are superimposed, so as to acquire a single wavelength-multiplexed image. The signal processing circuit utilizes information about the spatial distribution of spectral transmittance of the encoder so as to apply compressed sensing to the acquired wavelength-multiplexed image, thereby generating image data for each wavelength band. In the imaging device disclosed in U.S. Pat. No. 9,599,511, an optical filter array having at least two transmittance peaks (i.e., maximum values) within a target wavelength range is used as the encoder.

U.S. Pat. No. 9,466,628 discloses an example of a filter array including a Fabry-Perot resonator in which a dielectric multilayer film is used as a reflective layer. Japanese Unexamined Patent Application Publication No. 2018-107731 discloses an example of a filter array including various types of color filters.

SUMMARY

One non-limiting and exemplary embodiment provides a light detection system that can improve the spectral resolution of a hyperspectral camera, and a filter array used in the light detection system.

In one general aspect, the techniques disclosed here feature a filter array used in a light detection device that generates image data corresponding to each of N wavelength bands (N being an integer greater than or equal to 2) included in a specific wavelength range. The filter array includes optical filters. The optical filters include various types of optical filters with different light transmittance with respect to each of the N wavelength bands. M_i≥0.1 with respect to each of the N wavelength bands, where M_i=μ_i−σ_i, μ_i denoting an average value of light transmittance of the optical filters with respect to light having a wavelength included in an i-th wavelength band (i being an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, σ_i denoting a standard deviation of the light transmittance of the optical filters with respect to the light having the wavelength included in the i-th wavelength band.

According to the technique of the present disclosure, the spectral resolution of a hyperspectral camera can be improved.

General or specific aspects of the present disclosure may be implemented as a system, a device, a method, an integrated circuit, a computer program, or a storage medium, such as a computer-readable storage disk, or may be implemented as a freely-chosen combination of a system, a device, a method, an integrated circuit, a computer program, and a storage medium. The computer-readable storage medium may include a nonvolatile storage medium, such as a CD-ROM (compact disc-read only memory). The device may be constituted of one or more devices. If the device is constituted of two or more devices, the two or more devices may be disposed within a single apparatus, or may be disposed separately within two or more separate apparatuses. In this description and the claims, the term “device” may refer not only to a single device but also to a system formed of devices.

Additional benefits and advantages of the disclosed embodiments will become apparent from the specification and drawings. The benefits and/or advantages may be individually obtained by the various embodiments and features of the specification and drawings, which need not all be provided in order to obtain one or more of such benefits and/or advantages.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A schematically illustrates a light detection system according to an exemplary embodiment;

FIG. 1B illustrates a configuration example of the light detection system in which a filter array is disposed away from an image sensor;

FIG. 1C illustrates a configuration example of the light detection system in which the filter array is disposed away from the image sensor;

FIG. 1D illustrates a configuration example of the light detection system in which the filter array is disposed away from the image sensor;

FIG. 2A schematically illustrates an example of a filter array according to an exemplary embodiment;

FIG. 2B illustrates an example of a spatial distribution of light transmittance in each of wavelength bands included in a target wavelength range;

FIG. 2C illustrates an example of a transmission spectrum of a certain filter included in the filter array illustrated in FIG. 2A;

FIG. 2D illustrates an example of a transmission spectrum of another filter included in the filter array illustrated in FIG. 2A;

FIG. 3A is a diagram for explaining an example of the relationship between the target wavelength range and wavelength bands included therein;

FIG. 3B is a diagram for explaining another example of the relationship between the target wavelength range and the wavelength bands included therein;

FIG. 4A is a diagram for explaining the characteristic of a transmission spectrum of a certain filter in the filter array;

FIG. 4B illustrates a result obtained by averaging the transmission spectrum illustrated in FIG. 4A for each wavelength band;

FIG. 5A schematically illustrates a spatial pattern of light transmittance with respect to each of the wavelength bands in the filter array;

FIG. 5B schematically illustrates an example of a transmittance histogram that the filter array has with respect to an i-th wavelength band;

FIG. 6A schematically illustrates an example of a captured image having random noise superimposed on an original image;

FIG. 6B schematically illustrates the relationship of Expression (1) in which captured image data containing the random noise is expressed as a product of a matrix and spectral image data;

FIG. 7A illustrates an example of a transmission spectrum of a certain filter included in a filter array different from that in this embodiment;

FIG. 7B illustrates a mean square error (MSE) between a ground truth image and a spectral image in each of five wavelength bands in a case where an image captured using the filter array different from that in this embodiment contains random noise;

FIG. 8 illustrates the relationship between an average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μ_i−σ_i in a case where σ_i=0.08 with respect to each wavelength band;

FIG. 9A illustrates the relationship between an average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μ_i−σ_i in a case where σ_i=0.05 with respect to each wavelength band;

FIG. 9B illustrates the relationship between an average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μ_i−σ_i in a case where σ_i=0.07 with respect to each wavelength band;

FIG. 9C illustrates the relationship between an average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μ_i−σ_i in a case where σ_i=0.1 with respect to each wavelength band;

FIG. 10A is a cross-sectional view schematically illustrating a first example of the light detection device;

FIG. 10B is a cross-sectional view schematically illustrating a second example of the light detection device;

FIG. 11A schematically illustrates an example of a filter illustrated in FIG. 10A;

FIG. 11B illustrates an example of transmission spectra that a single-sided distributed Bragg reflector (DBR) structure and a double-sided DBR structure have when light vertically enters the structures;

FIG. 12A is a cross-sectional view schematically illustrating a third example of the light detection device;

FIG. 12B is a cross-sectional view schematically illustrating a fourth example of the light detection device;

FIG. 13A is a cross-sectional view schematically illustrating a fifth example of the light detection device;

FIG. 13B is a perspective view schematically illustrating an example of a sub filter array and a light detection element; and

FIG. 14 illustrates an example of transmission spectra of eight types of sub filter arrays.

DETAILED DESCRIPTIONS

Exemplary embodiments of the present disclosure will be described below. The embodiments to be described below indicate general or specific examples. Numerical values, shapes, components, positions and connection methods of the components, steps, and the sequence of the steps are examples and are not intended to limit the scope of the present disclosure. Of the components in the following embodiments, a component not defined in the independent claim indicating the most generic concept is described as a freely-chosen component. Furthermore, the drawings are not necessarily exact illustrations. In each drawing, same reference signs are given to substantially identical components, and redundant descriptions may sometimes be omitted or simplified.

Before describing the embodiments of the present disclosure, the underlying knowledge forming the basis of the present disclosure will be described.

U.S. Pat. No. 9,599,511 discloses an imaging device capable of generating high-resolution multi-wavelength images, that is, images with respect to individual wavelength bands. In this imaging device, an image of light from a target object is encoded by an optical element called an “encoder” and is captured. The encoder has, for example, two-dimensionally-arranged regions. A transmission spectrum of each of at least two of the regions has a maximum transmittance value in each of wavelength ranges within an imaging-target wavelength range. For example, the regions may respectively be disposed in correspondence with pixels of an image sensor. In an imaging process using the aforementioned encoder, data of each pixel contains information about the wavelength ranges. In other words, image data acquired in the imaging process is data containing compressed wavelength information. Therefore, the amount of data can be minimized by simply retaining two-dimensional data. For example, even in a case where a storage medium is limited in capacity, long-duration moving-image data can be acquired. The multi-wavelength images are generated by performing a reconstruction process involving reconstructing the image captured in the imaging process to generate images respectively corresponding to the wavelength ranges. In the following description, each of the images generated and corresponding one-to-one to the wavelength ranges, that is, wavelength bands, may also be referred to as “spectral image”.

The encoder may be realized by, for example, a filter array including two-dimensionally-arranged filters. For example, each filter may have the structure of a so-called Fabry-Perot resonator that includes two reflective layers and an interference layer located therebetween. As a Fabry-Perot resonator, for example, the structure disclosed in U.S. Pat. No. 9,466,628 may be employed. The filters may be designed such that the transmission spectrum of each filter has peaks in the imaging-target wavelength range. Alternatively, the filters may include, for example, the various types of color filters disclosed in Japanese Unexamined Patent Application Publication No. 2018-107731.

An image actually captured using an encoder may contain random noise, such as optical shot noise. Random noise deteriorates the spectral resolution of a spectral image generated in a reconstruction process. There is room for improvement in filter arrays that reduce the effect of random noise.

A filter array according to an embodiment of the present disclosure includes filters in which the light transmittance within an imaging-target wavelength range is appropriately designed. Such a filter array reduces the possibility in which the spectral resolution of a hyperspectral camera decreases due to random noise. A filter array according to an embodiment of the present disclosure and a light detection system according to the present disclosure equipped with the filter array will be briefly described below.

First Item

A filter array according to a first item is used in a light detection device that generates image data corresponding to each of N wavelength bands (N being an integer greater than or equal to 2) included in a specific wavelength range. The filter array includes optical filters. The optical filters include various types of optical filters with different light transmittance with respect to each of the N wavelength bands. M_i≥0.1 with respect to each of the N wavelength bands, where M_i=μ_i−σ_i, μ_i denoting an average value of light transmittance of the optical filters with respect to light having a wavelength included in an i-th wavelength band (i being an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, σ_i denoting a standard deviation of the light transmittance of the optical filters with respect to the light having the wavelength included in the i-th wavelength band. N may be an integer greater than or equal to 4.

In this filter array, an effect that random noise has on a spectral image is suppressed, so that the spectral resolution of a hyperspectral camera can be improved.

Second Item

In the filter array according to the first item, σ_i≥0.05 may be satisfied with respect to each of the N wavelength bands.

In this filter array, the filters can be readily distinguished from each other, so that the spectral-image reconstruction accuracy can be improved.

Third Item

In the filter array according to the first or second item, μ_i≥0.2 may be satisfied with respect to each of the N wavelength bands.

In this filter array, the transmittance is increased so that noise immunity can be improved, that is, an image reconstruction error occurring when noise is superimposed on image data acquired by image-capturing can be suppressed.

Fourth Item

In the filter array according to any one of the first to third items, M_max/M_min·≤3 may be satisfied, where M_max and M_min denote a maximum M_i and a minimum M_i, respectively, with respect to the N wavelength bands.

In this filter array, a variation in the spectral-image reconstruction accuracy between the wavelength bands can be suppressed.

Fifth Item

In the filter array according to any one of the first to fourth items, at least one optical filter of the optical filters may include an interference layer having a first surface and a second surface opposite the first surface, and a reflective layer provided on the first surface. A transmission spectrum of the at least one optical filter may have maximum values in the specific wavelength range. The reflective layer need not be provided on the second surface.

In this filter array, M_i≥0.1 can be satisfied in accordance with a specific structure.

Sixth Item

In the filter array according to the fifth item, the reflective layer may include at least one selected from the group consisting of a distributed Bragg reflector and a metallic film.

In this filter array, a reflective layer that efficiently reflects light within the specific wavelength range can be realized.

Seventh Item

In the filter array according to the sixth item, the distributed Bragg reflector may include at least one set of a first refractive-index layer and a second refractive-index layer. A refractive index of the first refractive-index layer may be higher than a refractive index of the second refractive-index layer.

In this filter array, the reflectance of the distributed Bragg reflector can be appropriately designed by adjusting the number of sets of first refractive-index layers and second refractive-index layers.

Eighth Item

In the filter array according to the seventh item, the first refractive-index layer may have a thickness of λ(4n_H), the second refractive-index layer may have a thickness of λ(4n_L), and the interference layer may have a thickness larger than λ/(2n_H), where λ denotes a wavelength included in the specific wavelength range, n_H denotes the refractive index of the first refractive-index layer, and n_L denotes the refractive index of the second refractive-index layer.

In this filter array, light having the wavelength λ can be efficiently reflected.

Ninth Item

In the filter array according to the sixth item, the metallic film may have a thickness larger than or equal to 1 nm and smaller than or equal to 100 nm.

In this filter array, the transmittance of the metallic film can be increased by appropriately adjusting the thickness of the metallic film.

Tenth Item

In the filter array according to any one of the first to fourth items, the light detection device may include an image sensor. The filter array may be disposed such that light transmitted through the optical filters enters the image sensor. At least one of the optical filters may be a sub filter array including two-dimensionally-arranged sub filters. The sub filter array may include various types of first sub filters having different transmission wavelength ranges and one or more second sub filters or openings each transmitting N light beams having a wavelength included in a corresponding wavelength band of the N wavelength bands. A percentage of an area of the one or more second sub filters or openings occupying a total area of the sub filter array may be higher than or equal to 4%.

In this filter array, M_i≥0.1 can be satisfied in accordance with a specific structure.

Eleventh Item

In the filter array according to the tenth item, the various types of first sub filters may include a red filter, a green filter, and a blue filter.

In this filter array, M_i≥0.1 can be satisfied in accordance with the first sub filters including RGB color filters.

Twelfth Item

A light detection system according to a twelfth item includes the filter array according to any one of the first to eleventh items and an image sensor that is disposed at a position where the image sensor receives light transmitted through the optical filters and that has sensitivity to light having a wavelength included in the specific wavelength range.

In this light detection system, a hyperspectral camera with improved spectral resolution and increased detection light intensity can be realized.

Thirteenth Item

The light detection system according to the twelfth item may further include a processing circuit that generates the image data based on data indicating a spatial distribution of the light transmittance of the optical filters and compressed image data acquired by the image sensor.

In the present disclosure, each circuit, unit, device, member, or section or each functional block in each block diagram may entirely or partially be implemented by, for example, one or more electronic circuits containing a semiconductor device, semiconductor IC (integrated circuit), or LSI (large scale integration). The LSI or the IC may be integrated in a single chip or may be configured by combining chips. For example, the functional blocks excluding storage elements may be integrated in a single chip. Although the terms “LSI” and “IC” are used here, the terms used may change depending on the degree of integration, such that so-called “system LSI”, “VLSI” (very large scale integration), or “ULSI” (ultra large scale integration) may be used. A field programmable gate array (FPGA) to be programmed after the LSI is manufactured, or a reconfigurable logic device that can reconfigure the connection relationship inside the LSI or can set up the circuit sections inside the LSI can also be used for the same purpose.

Furthermore, the function or operation of each circuit, unit, device, member, or section may entirely or partially be implemented by software processing. In this case, the software is stored in a non-transitory storage medium, such as one or more ROM (read-only memory) units, an optical disk, or a hard disk drive. When the software is executed by a processor, a function specified by the software is implemented by the processor and a peripheral device. A system or a device may include one or more non-transitory storage media storing the software, a processor, and a required hardware device, such as an interface.

Embodiments

Light Detection System

FIG. 1A schematically illustrates a light detection system 400 according to an exemplary embodiment of the present disclosure. The light detection system 400 includes an optical unit 40, a filter array 10, an image sensor 60, and a processing circuit 200. The filter array 10 has a function similar to that of the “encoder” disclosed in U.S. Pat. No. 9,599,511. Therefore, the filter array 10 may also be referred to as an “encoder”. The optical unit 40 and the filter array 10 are disposed on an optical path of light incident from a target object 70. In the example illustrated in FIG. 1A, the filter array 10 is disposed between the optical unit 40 and the image sensor 60.

In FIG. 1A, an apple is illustrated as an example of the target object 70. The target object 70 is not limited to an apple and may be a freely-chosen object. Based on image data generated by the image sensor 60, the processing circuit 200 generates image data with respect to each of wavelength bands included in a specific wavelength range (also referred to as “target wavelength range” hereinafter). This image data will be referred to as “spectral image data” in this description. The number of wavelength bands included in the target wavelength range will be defined as N (N being an integer greater than or equal to 4). In the following description, the spectral image data to be generated with respect to the wavelength bands will be referred to as spectral images 220W₁, 220W₂, . . . , and 220W_N, and these spectral images will collectively be referred to as spectral images 220. In this description, a signal indicating an image, that is, a group of signals indicating pixel values of pixels constituting an image, may sometimes be simply referred to as “image”.

The filter array 10 includes translucent filters arranged in rows and columns. The filter array 10 is an optical element in which the light transmission spectrum, that is, wavelength dependency with respect to light transmittance, varies from filter to filter. The filter array 10 modulates the intensity of incident light for each wavelength band and allows the incident light to pass through.

In the example illustrated in FIG. 1A, the filter array 10 is disposed close to or directly on the image sensor 60. The expression “close to” implies that the filter array 10 is close to the image sensor 60 to an extent that an image of light from the optical unit 40 is formed on a surface of the filter array 10 in a state where the image is clear to a certain extent. The expression “directly on” implies that the two are close to each other with hardly any gap therebetween. The filter array 10 and the image sensor 60 may be integrated with each other. In this description, a device that includes the filter array 10 and the image sensor 60 will be referred to as “light detection device 300”.

The optical unit 40 includes at least one lens. Although illustrated as a single lens in FIG. 1A, the optical unit 40 may be constituted of a combination of lenses. The optical unit 40 forms an image on an imaging surface of the image sensor 60 via the filter array 10.

The filter array 10 may be disposed away from the image sensor 60. FIGS. 1B to 1D each illustrate a configuration example of the light detection system 400 in which the filter array 10 is disposed away from the image sensor 60. In the example in FIG. 1B, the filter array 10 is disposed at a position located between the optical unit 40 and the image sensor 60 and away from the image sensor 60. In the example in FIG. 1C, the filter array 10 is disposed between the target object 70 and the optical unit 40. In the example in FIG. 1D, the light detection system 400 includes two optical units 40A and 40B, and the filter array 10 is disposed therebetween. As in these examples, an optical unit including at least one lens may be disposed between the filter array 10 and the image sensor 60. The filter array 10, the optical unit 40, and the image sensor 60 may have atmospheric air filling the spaces therebetween, or may be sealed with gas, such as nitrogen gas.

The image sensor 60 includes two-dimensionally-arranged light detection elements. The image sensor 60 may be, for example, a CCD (charge-coupled device) sensor, a CMOS (complementary metal oxide semiconductor) sensor, or an infrared array sensor. The light detection elements may include, for example, photodiodes. The image sensor 60 may be, for example, a monochrome-type sensor or a color-type sensor. The target wavelength range may be set arbitrarily. The target wavelength range is not limited to a visible wavelength range, and may be an ultraviolet, near-infrared, mid-infrared, far-infrared, or microwave wavelength range.

In the example illustrated in FIG. 1A, each light detection element is disposed facing one of the filters. Each light detection element has sensitivity to light in the imaging-target wavelength range. In detail, each light detection element has substantial sensitivity required for detecting light in the imaging-target wavelength range. For example, the external quantum efficiency of each light detection element in the aforementioned wavelength range may be higher than or equal to 1%. The external quantum efficiency of each light detection element may be higher than or equal to 10%. The external quantum efficiency of each light detection element may be higher than or equal to 20%. In the following description, each light detection element may also be referred to as “pixel”.

The processing circuit 200 may be, for example, an integrated circuit that includes a processor and a storage medium, such as a memory. Based on an image 120 acquired by the image sensor 60, the processing circuit 200 generates data of the spectral images 220 individually containing information about the wavelength bands. The spectral images 220, as well as a method for processing an image signal in the processing circuit 200, will be described in detail later. The processing circuit 200 may be incorporated in the light detection device 300, or may be a component of a signal processing device electrically connected to the light detection device 300 in a wired or wireless manner.

Filter Array

The filter array 10 according to this embodiment will be described below. The filter array 10 is disposed on the optical path of light incident from a target object and modulates the intensity of the incident light for each wavelength before outputting the light. This process performed by a filter array, that is, an encoder, is referred to as “encoding” in this description.

FIG. 2A schematically illustrates an example of the filter array 10. The filter array 10 includes two-dimensionally-arranged filters. Each filter has an individually-set transmission spectrum. The transmission spectrum is expressed as a function T(λ), where λ denotes the wavelength of incident light. The transmission spectrum T(λ) may have a value greater than or equal to 0 and less than or equal to 1.

In the example illustrated in FIG. 2A, the filter array 10 has 48 rectangular filters arranged in a 6 row by 8 column matrix. This is merely an example, and a larger number of filters may be set in an actual application. For example, the number may be about the same as the number of pixels in the image sensor 60. The number of filters included in the filter array 10 is set in accordance with the intended usage within a range of, for example, several tens to several thousands of filters.

FIG. 2B illustrates an example of a spatial distribution of light transmittance for each of wavelength bands W1, W2, . . . , and Wi included in the target wavelength range. In the example illustrated in FIG. 2B, the differences in the gradation levels of the filters indicate differences in transmittance. A paler filter has higher transmittance, whereas a darker filter has lower transmittance. As illustrated in FIG. 2B, the spatial distribution of light transmittance varies from wavelength band to wavelength band.

FIGS. 2C and 2D illustrate examples of transmission spectra of a filter A1 and a filter A2 included in the filters of the filter array 10 in FIG. 2A. The transmission spectrum of the filter A1 and the transmission spectrum of the filter A2 are different from each other. Accordingly, the transmission spectrum of the filter array 10 varies from filter to filter. However, not all the filters need to have different transmission spectra. In the filter array 10, at least two of the filters have transmission spectra different from each other. In other words, the filter array 10 includes two or more filters with different transmission spectra. In one example, the number of transmission spectrum patterns of the filters included in the filter array 10 may be equal to or greater than the number i of wavelength bands included in the target wavelength range. The filter array 10 may be designed such that at least half of the filters have different transmission spectra.

FIGS. 3A and 3B are diagrams for explaining the relationship between a target wavelength range W and the wavelength bands W1, W2, . . . , and Wi included therein. The target wavelength range W may be set to any of various ranges in accordance with the intended usage. For example, the target wavelength range W may be a visible-light wavelength range from approximately 400 nm to approximately 700 nm, a near-infrared wavelength range from approximately 700 nm to approximately 2500 nm, or a near-ultraviolet wavelength range from approximately 10 nm to approximately 400 nm. Alternatively, the target wavelength range W may be a radio-wave range, such as a mid-infrared, far-infrared, terahertz-wave, or millimeter-wave range. Accordingly, the wavelength range to be used is not limited to a visible-light range. In this description, nonvisible light, such as a near-ultraviolet ray, a near-infrared ray, and a radio wave, in addition to visible light will be referred to as “light” for the sake of convenience.

In the example illustrated in FIG. 3A, the target wavelength range W is equally divided by i into a wavelength band W1, a wavelength band W2, . . . , and a wavelength band Wi, where i denotes a freely-chosen integer greater than or equal to 4. However, the example is not limited to this. The wavelength bands included in the target wavelength range W may be set arbitrarily. For example, the bandwidths may be nonuniform among the wavelength bands. There may be a gap between neighboring wavelength bands. In the example illustrated in FIG. 3B, the bandwidth varies from wavelength band to wavelength band, and a gap exists between two neighboring wavelength bands. Accordingly, the wavelength bands may be different from each other, and may be set arbitrarily. The division number i for the wavelengths may be less than or equal to 3.

FIG. 4A is a diagram for explaining the characteristic of a transmission spectrum of a certain filter in the filter array 10. In the example illustrated in FIG. 4A, the transmission spectrum has a maximum value P1 to a maximum value P5 and minimum values with respect to wavelengths within the target wavelength range W. In the example illustrated in FIG. 4A, the light transmittance within the target wavelength range W is normalized such that the maximum value thereof is 1 and the minimum value thereof is 0. In the example illustrated in FIG. 4A, the transmission spectrum has maximum values in wavelength bands, such as the wavelength band W2 and a wavelength band Wi−1. Accordingly, in this embodiment, the transmission spectrum of each filter has maximum values in at least two wavelength bands from the wavelength band W1 to the wavelength band Wi. It is apparent from FIG. 4A that the maximum value P1, the maximum value P3, the maximum value P4, and the maximum value P5 are greater than or equal to 0.5.

Accordingly, the light transmittance of each filter varies from wavelength to wavelength. Therefore, the filter array 10 transmits a large amount of incident light in certain wavelength bands and does not transmit much of the incident light in other wavelength bands. For example, the transmittance with respect to light in k wavelength bands among i wavelength bands may be higher than 0.5, whereas the transmittance with respect to light in the remaining (i−k) wavelength bands may be lower than 0.5. In this case, k denotes an integer satisfying the relationship 2≤k<i. Supposing that the incident light is white light uniformly containing all wavelength components of visible light, the filter array 10 modulates the incident light into light having discrete intensity peaks with respect to the wavelengths for each filter, superimposes the multi-wavelength light, and outputs the light.

FIG. 4B illustrates an example of a result obtained by averaging the transmission spectrum illustrated in FIG. 4A for each of the wavelength band W1, the wavelength band W2, and the wavelength band Wi. Averaged transmittance is obtained by integrating the transmission spectrum T(λ) for each wavelength band and dividing the integral value by the bandwidth of the wavelength band. In this description, a transmittance value averaged for each wavelength band in this manner will be referred to as transmittance in that wavelength band. In this example, transmittance is outstandingly high in the three wavelength bands having the maximum value P1, the maximum value P3, and the maximum value P5. In particular, the transmittance exceeds 0.8 in the two wavelength bands having the maximum value P3 and the maximum value P5.

The resolution in the wavelength direction of the transmission spectrum of each filter may be set to about the bandwidth of a desired wavelength band. In other words, in a wavelength range including one maximum value in a transmission spectrum curve, the width of a range having a value greater than or equal to an average value between a minimum value closest to the maximum value and the maximum value may be set to about the bandwidth of the desired wavelength band. In this case, the transmission spectrum may be decomposed into frequency components by, for example, a Fourier transform, so that the value of a frequency component corresponding to the wavelength band relatively increases.

As illustrated in FIG. 2A, the filter array 10 typically has filters segmented into a grid-like pattern. These filters partially or entirely have transmission spectra different from each other. The light-transmittance wavelength distribution and spatial distribution of the filters included in the filter array 10 may be, for example, a random distribution or a semi-random distribution.

The concepts of a random distribution and a semi-random distribution are as follows. First, each filter in the filter array 10 may be regarded as, for example, a vector component having a value of 0 to 1 in accordance with the light transmittance. In a case where the transmittance is 0, the value of the vector component is 0. In a case where the transmittance is 1, the value of the vector component is 1. In other words, a group of filters arranged in a single line in the row direction or the column direction may be regarded as a multidimensional vector having a value from 0 to 1. Therefore, it may be regarded that the filter array 10 includes multidimensional vectors in the row direction or the column direction. In this case, a random distribution means that two freely-chosen multidimensional vectors are independent, that is, not parallel. A semi-random distribution means that the multidimensional vectors partially include a non-independent configuration. Therefore, in a random distribution and a semi-random distribution, a vector having a light transmittance value in a first wavelength band as an element in each filter belonging to a group of filters included in the filters and arranged in one row or column and a vector having a light transmittance value in the first wavelength band as an element in each filter belonging to a group of filters arranged in another row or column are independent from each other. With regard to a second wavelength band different from the first wavelength band, a vector having a light transmittance value in the second wavelength band as an element in each filter belonging to a group of filters included in the filters and arranged in one row or column and a vector having a light transmittance value in the second wavelength band as an element in each filter belonging to a group of filters arranged in another row or column are independent from each other.

In a case where the filter array 10 is disposed close to or directly on the image sensor 60, the spacing between the filters included in the filter array 10 may substantially match the pixel pitch of the image sensor 60. Accordingly, the resolution of an encoded image of light output from the filter array 10 substantially matches the resolution of pixels. Light transmitted through each filter enters only a single corresponding pixel, so that an arithmetic process to be described later can be readily performed. In a case where the filter array 10 is disposed away from the image sensor 60, the pitch of the filters may be set finely in accordance with the distance.

In the examples illustrated in FIGS. 2A to 2D, the filter array 10 has a gray-scale transmittance distribution in which the transmittance of each filter may be a freely-chosen value that is greater than or equal to 0 and less than or equal to 1. However, such a gray-scale transmittance distribution is not necessarily essential. For example, a binary-scale transmittance distribution in which the transmittance of each filter may have a value of either substantially 0 or substantially 1 may be employed. In a binary-scale transmittance distribution, each filter transmits a large portion of light in at least two wavelength bands of the wavelength bands included in the target wavelength range, and does not transmit a large portion of light in the remaining wavelength bands. The expression “large portion” refers to substantially 80% or more.

Of all the filters, some of them, such as half of the filters, may be replaced with transparent filters. Such transparent filters transmit light in all the wavelength bands W1 to Wi included in the target wavelength range with about the same high transmittance. For example, the high transmittance is higher than or equal to 0.8. In such a configuration, the transparent filters may be arranged in, for example, a checkboard pattern. In other words, in two arrangement directions of the filters in the filter array 10, filters whose light transmittance varies in accordance with the wavelength and transparent filters may be alternately arranged. In the example illustrated in FIG. 2A, the two arrangement directions are a horizontal direction and a vertical direction.

Such data indicating the spatial distribution of the spectral transmittance of the filter array 10 is preliminarily acquired based on design data or actual measurement calibration, and is stored in a storage medium included in the processing circuit 200. The data is used in an arithmetic process to be described later.

The filter array 10 may be constituted by using, for example, a multilayer film, an organic material, a diffraction grating structure, or a metal-containing micro-structure. In a case where a multilayer film is to be used, for example, a dielectric multilayer film or a multilayer film including a metallic layer may be used. In this case, the filter array 10 may be formed such that at least one of the thickness, the material, and the stacked order of each multilayer film varies for each filter. Accordingly, spectral characteristics that vary from filter to filter can be realized. By using a multilayer film, a sharp rise and fall of the spectral transmittance can be realized. A configuration that uses an organic material may be realized by varying a contained pigment or dye from filter to filter, or by stacking different types of materials. A configuration that uses a diffraction grating structure may be realized by providing a diffracting structure with a diffraction pitch or depth that varies from filter to filter. In a case where a metal-containing micro-structure is to be used, the filter array 10 may be fabricated by utilizing spectroscopy based on a plasmon effect.

Processing Circuit

Next, a method for generating multi-wavelength spectral images 220 in a reconstruction process by using the processing circuit 200 will be described. The term “multi-wavelength” refers to, for example, wavelength bands larger in number than the three color wavelength bands of RGB acquired by a normal color camera. The number of wavelength bands may be, for example, four to about 100. The number of wavelength bands may also be referred to as “the number of spectral bands”. Depending on the intended usage, the number of spectral bands may exceed 100.

Data to be desirably obtained is a spectral image 220, and the data is expressed as f. Assuming that the number of spectral bands is defined as w, f is data obtained by integrating image data f₁, f₂, . . . , and f_w of respective bands. As illustrated in FIG. 1A, the horizontal direction of an image is defined as an x direction, and the vertical direction of an image is defined as a y direction. Assuming that the number of pixels in the x direction of image data to be obtained is defined as n and the number of pixels in they direction is defined as m, each piece of image data f₁, f₂, . . . , and f_w is two-dimensional data with n×m pixels. Therefore, data f is three-dimensional data with n×m×w elements. On the other hand, the number of elements in data g of the image 120 acquired by being encoded and multiplexed by the filter array 10 is n×m. The data g can be expressed using Expression (1) indicated below:

$\begin{array}{cc}ℊ=\mathrm{Hf}=H\left[\begin{array}{c}{f}_1\\ f_2\\ ⋮\\ f_w\end{array}\right]& \left(1\right)\end{array}$

In this case, f₁, f₂, . . . , and f_w each denote data having n×m elements. Therefore, a vector at the right-hand side is strictly a one-dimensional vector of n×m×w rows and one column. A vector g is expressed and calculated by being converted into a one-dimensional vector of n×m rows and one column. A matrix H expresses a transform involving encoding and intensity-modulating components f₁, f₂, . . . , and f_w of a vector f with encoding information that varies for each wavelength band and adding the components together. Therefore, H is a matrix of n×m rows and n×m×w columns.

If the vector g and the matrix H are given, it appears as if f can be calculated by solving an inverse problem of Expression (1). However, since the number of elements n×m×w in the data f to be obtained is greater than the number of elements n×m in the acquisition data g, this problem is an ill-posed problem and cannot be solved as is. The processing circuit 200 utilizes the redundancy of the image included in the data f to obtain a solution by using a compressed sensing technique. In detail, the data f to be obtained is estimated by solving Expression (2) indicated below.

$\begin{array}{cc}{f}^{\prime }=\underset{f}{\arg \min }\left\{{ℊ-\mathrm{Hf}}_{l_2}+\mathrm{\tau \Phi }\left(f\right)\right\}& \left(2\right)\end{array}$

In this case, f′ denotes data of estimated f. The first term in the parentheses in the above expression indicates an amount of deviation, that is, a so-called residual term, between an estimation result Hf and the acquisition data g. Although a square sum is set as the residual term here, an absolute value or a root-sum-square value may be set as the residual term. The second term in the parentheses is a regularization term or a stabilization term to be described later. Expression (2) involves determining f that minimizes the sum of the first term and the second term. The processing circuit 200 can converge on solution in accordance with a recursive iterative operation so as to ultimately calculate a solution f′.

The first term within the parentheses in Expression (2) indicates an arithmetic process involving determining a square sum of a difference between the acquisition data g and Hf obtained by performing a system conversion on fin the estimation process using the matrix H. In the second term, Φ(f) denotes a limiting condition in the regularization of f, and is a function having sparse information of the estimation data reflected therein. With regard to the function, there is an advantage of making the estimation data smooth or stable. The regularization term may be expressed by, for example, a discrete cosine transform (DCT) of f, a wavelet transform, a Fourier transform, or a total variation (TV). For example, if a total variation is used, stable estimation data in which the effect of noise in the observation data g is reduced can be acquired. The sparse characteristics of the target object 70 in the space of each regularization term vary depending on the texture of the target object 70. A regularization term in which the texture of the target object 70 becomes sparser in the space of the regularization term may be selected. Alternatively, regularization terms may be included in the arithmetic process. τ denotes a weighting factor. The larger the weighting factor τ, the amount of cutback of redundant data increases, thus increasing the compression ratio. The smaller the weighting factor τ, the weaker the convergence to the solution. The weighting factor τ is set to an appropriate value at which f converges to a certain extent and that does not lead to over-compression.

In the configurations in FIGS. 1B to 1D, an image encoded by the filter array 10 is acquired in a blurry state on the imaging surface of the image sensor 60. Therefore, by preliminarily storing this blurriness information and reflecting this blurriness information on the aforementioned system matrix H, spectral images 220 can be generated in a reconstruction process. The blurriness information can be expressed by a point spread function (PSF). A PSF is a function that defines the degree of spreading of a point image toward surrounding pixels. For example, if a point image corresponding to one pixel in an image spreads to a k×k pixel region surrounding the pixel due to blurriness, the PSF may be defined as a coefficient group, that is, a matrix, indicating an effect on the pixels within the region. By reflecting the effect of blurriness of the encoding pattern by the PSF on the system matrix H, spectral images 220 can be generated in a reconstruction process. Although the filter array 10 may be disposed at a freely-chosen position, a position where the encoding pattern of the filter array 10 does not spread too much and disappear may be selected.

Although an arithmetic example using compressed sensing indicated in Expression (2) is described here, a solution may be obtained by using another method. For example, another statistical method, such as a maximum likelihood estimation method or a Bayes estimation method, may be used. Furthermore, the number of spectral images 220 is arbitrary, and the wavelength bands may also be set arbitrarily. The reconstruction method is disclosed in detail in U.S. Pat. No. 9,599,511. The entire disclosure contents of U.S. Pat. No. 9,599,511 are incorporated in this description.

Feature Values of Filter Array 10

An image actually captured by using the filter array 10 may contain random noise called optical shot noise. Random noise increases in proportion to the square root of the detection light intensity. Feature values that the filter array 10 according to this embodiment have and that are used for discussing random noise, to be described later, will be described here with reference to FIGS. 5A and 5B. FIG. 5A schematically illustrates a spatial pattern of light transmittance with respect to each of the wavelength bands in the filter array 10. The spatial pattern is expressed as a mosaic pattern. The number of wavelength bands will be defined as N (N being an integer greater than or equal to 4). As illustrated in FIG. 5A, the light-transmittance distribution of the filter array 10 varies for each wavelength band. FIG. 5B schematically illustrates an example of a transmittance histogram that the filter array 10 has with respect to an i-th wavelength band (i being an integer greater than or equal to 1 and less than or equal to N). In the example illustrated in FIG. 5B, the abscissa axis indicates transmittance, whereas the ordinate axis denotes the number of filters having the transmittance. From the histogram illustrated in FIG. 5B, an average transmittance value μ_i of light in the i-th wavelength band and a finite standard deviation σ_i are obtained as the feature values of the filter array 10. If the histogram illustrated in FIG. 5B has a Gaussian distribution, the number of filters with transmittance included within a range greater than or equal to μ_i−σ_i and less than or equal to μ_i+σ_i occupies approximately 68% of the total. The number of filters with transmittance included within a range greater than or equal to μ_i−2σ_i and less than or equal to μ_i+2σ_i occupies approximately 95% of the total. As illustrated in FIG. 5B, the number of filters having high transmittance increases as the value of μ_i−2σ_i increases. The filters 100 can be readily distinguished from each other as σ_i increases.

To obtain a histogram, the transmittance of each optical filter in the filter array 10 is measured by using a light detector that measures the light intensity based on a predetermined gray-scale value. For example, a histogram can be obtained by using a light detector, such as an image sensor, capable of detecting a two-dimensional light-intensity distribution based on a predetermined gray-scale value, such as 8 bits or 16 bits. In detail, the transmittance of light in the i-th wavelength band of each filter 100 in the filter array 10 can be determined from the ratio between the intensity of light in the i-th wavelength band detected in a state where the filter array 10 is disposed and the intensity of light in the i-th wavelength band detected in a state where the filter array 10 is not disposed. The histogram as illustrated in FIG. 5B can be obtained from the data about the transmittance of each filter 100 acquired in accordance with the above-described method. In the actual filter array 10, a histogram with a shape different from that in FIG. 5B may possibly be obtained. Because the wavelength dependency with respect to transmittance varies from filter to filter, the shape of the histogram varies from wavelength band to wavelength band. Therefore, the average transmittance value of the filters 100 and the standard deviation also vary from wavelength band to wavelength band.

In the following description, it is assumed that the gray-scale value of the transmittance histogram is 8 bits. Supposing that the light intensity is detected based on a gray-scale value other than 8 bits, a transmittance histogram can still be determined by converting the intensity into the 8-bit gray-scale value.

Effect of Random Noise on Spectral Image

Next, an effect that random noise has on a spectral image will be described with reference to FIGS. 6A to 7B.

FIG. 6A schematically illustrates an example of a captured image having random noise superimposed on an original image. As illustrated in FIG. 6A, the captured image containing the random noise may possibly be blurry, as compared with the original image. FIG. 6B schematically illustrates the relationship of Expression (1) in which the captured image data g containing the random noise is expressed as a product of the matrix H and the spectral image data f. The matrix H illustrated in FIG. 6B includes components of the spatial distribution of the transmittance for each wavelength band illustrated in FIG. 5A.

FIG. 7A illustrates an example of a transmission spectrum of a certain filter included in a filter array different from that in this embodiment. In the example illustrated in FIG. 7A, the target wavelength range W is greater than or equal to 450 nm and less than or equal to 850 nm. The target wavelength range W includes five wavelength bands each having a bandwidth of 80 nm. In the example illustrated in FIG. 7A, the transmission spectrum has eight sharp peaks. The transmittance has a maximum value of approximately 1 and a minimum value of approximately 0.02. The transmittance between two neighboring peaks is sufficiently low. The filters 100 having such a transmission spectrum are each realized by a resonant cavity including two reflective layers with high reflectance within the target wavelength range W and an interference layer between the reflective layers. By changing the refractive index and/or the thickness of the interference layer, the transmission spectrum shifts toward the longer wavelength side or the shorter wavelength side. The filter array includes various types of filters with transmission spectra that have been shifted in this manner. The filter array includes 1,000,000 two-dimensionally-arranged filters. The 1,000,000 filters include 16 types of filters arranged in the random distribution or the semi-random distribution.

FIG. 7B illustrates a mean squared error (MSE) between a ground truth image and a spectral image in each of five wavelength bands in a case where an image captured using the aforementioned filter array contains random noise. The random noise has occurred in accordance with a Gaussian distribution in which the center is μ_noise=0 and the standard deviation is σ_noise. A random-noise variance N_noise to be added to each pixel is calculated by using Expression (3) indicated below:

$\begin{array}{cc}{N}_{\mathrm{noise}}=\frac{1}{\sqrt{2{\mathrm{\pi \sigma }}_{\mathrm{noise}}}}\exp \left(-\frac{{\left({ℊ}_{\mathrm{noise}}-{\mu }_{\mathrm{noise}}\right)}^2}{2{{\sigma }_{\mathrm{noise}}}^2}\right)& \left(3\right)\end{array}$

In this case, g_noise denotes a value of noise superimposed on each pixel and may be a positive value or a negative value. In the example illustrated in FIG. 7B, σ_noise=0, 5, and 10. σ_noise=0 implies that there is no random noise. The random noise increases with increasing σ_noise. The mean squared error is calculated by using Expression (4) indicated below.

$\begin{array}{cc}MSE=\frac{1}{N·M}\sum _{i=1}^N\sum _{j=1}^M{\left(I_{i,j}^{\prime }-I_{i,j}\right)}^2& \left(4\right)\end{array}$

In this case, N and M denote the number of pixels in the horizontal direction and the vertical direction, respectively. I_i,j denotes a pixel value of a pixel at a position (i, j) in the ground truth image. I′_i,j denotes a pixel value of a pixel at the position (i, j) in the spectral image.

As illustrated in FIG. 7B, it is apparent that the MSE in all of the five wavelength bands increases with increasing σ_noise. If there is no random noise, a filter having a transmission spectrum with a large contrast ratio between the maximum value and the minimum value of the transmittance can achieve an improved S/N ratio between the wavelength bands, as illustrated in FIG. 7A. In other words, the difference in the spatial distribution of the transmittance between the wavelength bands, illustrated in FIG. 5A, becomes clear. However, a filter array including such filters is susceptible to random noise. As a result, the spectral resolution of a hyperspectral camera may deteriorate.

Filter Array 10 Having Noise Immunity

The following description relates to the filter array 10 according to this embodiment that can solve the aforementioned problem. The filter array 10 in which the value of μ_i−2σ_i illustrated in FIG. 5B is large has noise immunity. This is because the transmittance is high in such a filter array 10. The filter array 10 in which σ_i illustrated in FIG. 5B is large also has noise immunity. This is due to improved spectral-image reconstruction accuracy since the variance of transmittance between the filters is large and the filters 100 can thus be readily distinguished from each other in such a filter array 10. Accordingly, the optical characteristics of the filter array 10 according to this embodiment will now be described by using M_i=μi−σ_i, which is a sum of μ_i−2σ_i and σ_i, as an indicator of noise immunity. Similar to the above-described example, the filter array 10 according to this embodiment includes various types of filters arranged in the random distribution or the semi-random distribution.

FIG. 8 illustrates the relationship between an average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μi−σ_i in a case where σ_i=0.08 with respect to each wavelength band. In the example illustrated in FIG. 8, the random-noise standard deviation σ_noise=0, 2, 3, 4, and 5. The amount of light transmitted through the filter array 10 is dependent on M_i. The amount of light transmitted through the filter array 10 decreases as the value of M_i decreases, whereas the amount of light transmitted through the filter array 10 increases as the value of M_i increases. If the filters 100 included in the filter array 10 mostly have low transmittance and partially have high transmittance, the transmittance histogram of the filter array 10 may possibly be asymmetric. In such a filter array 10, M_i may possibly be a negative value.

In a case where σ_noise=0, a captured image does not contain random noise. In this case, the average MSE is kept low when M_i≤0.45. As illustrated in FIG. 7A, if the contrast ratio of the transmittance in the filters 100 is high, an average amount of light transmitted through the filter array 10 is small, and the value of M_i is small. Such a filter array 10 increases the S/N ratio between the wavelength bands. As a result, an occurrence of a spectral-image reconstruction error can be suppressed. In contrast, when M_i≥0.45, the average MSE increases as M_i increases. If the contrast ratio of the transmittance in the filters 100 is low, the average amount of light transmitted through the filter array 10 is large, and the value of M_i is large. Such a filter array 10 decreases the S/N ratio between the wavelength bands. As a result, the spectral-image reconstruction error increases.

In a case where σ_noise>0, the average MSE increases greatly as σ_noise increases when M_i<0.2, as indicated with an elliptical region surrounded by a solid line. In contrast, when M_i is near 0.42, the average MSE increases as σ_noise increases, but the amount of increase thereof is suppressed, as indicated with an elliptical region surrounded by a dashed line. When M_i≥0.45, the average MSE increases as M_i increases even if an is small. As illustrated in FIG. 8, in a case where σ_noise=5, the average MSE may sometimes increase suddenly in a discontinuous fashion. The above characteristics are summarized as follows.

• • (If M_i is small) the S/N ratio between the wavelength bands is high. Therefore, when σ_noise is small, the spectral-image reconstruction accuracy is high. When σ_noise increases, the amount of random noise is not negligible, as compared with a small amount of light transmitted through the filter array 10. As a result, the spectral-image reconstruction accuracy greatly decreases.
  • (If M_i is too large) the S/N ratio between the wavelength bands is low. Therefore, the spectral-image reconstruction accuracy is low even if σ_noise is small.
  • (If M_i is reasonably large) the spectral-image reconstruction accuracy is high when σ_noise is small. Even if σ_noise increases, the amount of random noise does not increase much, as compared with the amount of light transmitted through the filter array 10. As a result, a decrease in the spectral-image reconstruction accuracy is suppressed.

FIGS. 9A to 9C each illustrate the relationship between the average MSE between a ground truth image and a spectral image in each of the wavelength bands and M_i=μ_i−σ_i in a case where σ_i=0.05, 0.07, and 0.1 with respect to each wavelength band. As illustrated in FIGS. 9A to 9C, in a case where M_i is reasonably large, a decrease in the spectral-image reconstruction accuracy is suppressed even when an increases. Such M_i is greater than or equal to approximately 0.3 and less than or equal to approximately 0.5. In actuality, there is a reconstruction error caused by other noise, such as read noise, of about several %, in addition to the reconstruction error caused by random noise. When the total reconstruction error exceeds 5%, the lowness of the spectral-image reconstruction accuracy may possibly become visible. Therefore, a permissible reconstruction error caused by random noise may possibly be, for example, more than or equal to 3%. In an 8-bit gray-scale, a reconstruction error of 3% is equal to an average MSE of 56. In the examples illustrated in FIGS. 9A to 9C, in a case where σ_noise=5 that resembles actual random noise, the lower limit for M_i when the average MSE falls below 56 is M_i=0.1. Accordingly, it may be regarded that the filter array 10 having M_i≥0.1 is robust against random noise.

In addition to having M_i≥0.1, the filter array 10 according to this embodiment has the following characteristics.

• • σ_i≥0.05 with respect to each of the wavelength bands. In this case, since the filters 100 are readily distinguishable from each other, the spectral-image reconstruction accuracy can be improved.
  • μ_i≥0.2 with respect to each of the wavelength bands. In this case, M_i≥0.1 is satisfied with respect to 0.05≤σ_i≤0.1 illustrated in FIGS. 8 to 9C.
  • M_max/M_min≤3, where a maximum M_i and a minimum M_i with respect to the wavelength bands are defined as M_max and M_min, respectively. In this case, a variation in the spectral-image reconstruction accuracy between the wavelength bands can be suppressed.

Specific Structure of Filter Array

Next, an example of a specific structure of the filter array 10 according to this embodiment that satisfies M_i≥0.1 with respect to each of the wavelength bands will be described with reference to FIGS. 10A and 10B. FIGS. 10A and 10B are cross-sectional views schematically illustrating a first example and a second example, respectively, of the light detection device 300. Each cross-sectional view illustrates an example of a cross-sectional structure of one of the rows of the filter array 10 illustrated in FIG. 2A and the image sensor 60. In the examples illustrated in FIGS. 10A and 10B, the filter array 10 is disposed on the image sensor 60. Light detection elements 60a included in the image sensor 60 are respectively positioned directly below the filters 100 included in the filter array 10. The filter array 10 and the image sensor 60 may be separated from each other. Even in that case, each light detection element 60a may be disposed at a position where it receives light transmitted through one of the filters. The components may be disposed such that light transmitted through the filters enters the light detection elements 60a via a mirror. In that case, each light detection element 60a is not disposed directly below one of the filters.

The filters 100 included in the filter array 10 according to this embodiment each have a structure of a resonant cavity. The structure of the resonant cavity refers to a structure in which light with a certain wavelength forms a standing wave and exists stably therein. A resonant cavity illustrated in FIG. 10A includes a substrate 22, a reflective layer 24, and an interference layer 26 stacked in this order. A resonant cavity illustrated in FIG. 10B includes a substrate 22, an interference layer 26, and a reflective layer 24 stacked in this order. The substrate 22 illustrated in each of FIGS. 10A and 10B is provided uniformly throughout all the filters 100 without any steps. Unlike the reflective layer 24 illustrated in FIG. 10B, the reflective layer 24 illustrated in FIG. 10A is provided uniformly throughout all the filters 100 without any steps. As illustrated in FIGS. 10A and 10B, the interference layer 26 and the reflective layer 24 may be stacked in a freely-chosen order. The substrate 22 is not necessarily essential. The reflective layer 24 may include, for example, a distributed Bragg reflector (DBR). The configuration of the reflective layer 24 will be described in detail later. The interference layer 26 has a different refractive index and/or a different thickness for each filter 100. The filters 100 have different transmission spectra depending on the refractive index and/or the thickness of the interference layer 26. The transmission spectrum of each filter 100 has maximum transmittance values at various wavelengths within the target wavelength range W.

In the filter array 10 according to this embodiment, at least one filter of the filters 100 may have the aforementioned resonant cavity, whereas the other filters do not have to have the aforementioned resonant cavity. For example, the filter array 10 may include a filter, such as a transparent filter or an ND filter (neutral density filter), not having wavelength dependency with respect to light transmittance.

In the first example, the interference layer 26 may be exposed to atmospheric air. Components, such as a lens and a protection cover, may be disposed above the surface of the interference layer 26 with a space therebetween. In this case, the space may be filled with atmospheric air, or may be sealed with gas, such as nitrogen gas. The same applies to the surface of the reflective layer 24 in the second example.

Next, an example of the configuration of each filter 100 will be described with reference to FIG. 11A. FIG. 11A schematically illustrates an example of each filter 100 illustrated in FIG. 10A. As illustrated in FIG. 11A, the reflective layer 24 includes a DBR in which first refractive-index layers 24a and second refractive-index layers 24b are alternately stacked. The DBR includes one or more pair layers of first refractive-index layers 24a and second refractive-index layers 24b having different refractive indices. The refractive index of the first refractive-index layers 24a is higher than the refractive index of the second refractive-index layers 24b. A distributed Bragg reflector has a wavelength range with high reflectance in accordance with Bragg reflection occurring due to a periodical structure. Such a wavelength range is also called a stop band. When the number of aforementioned pair layers is increased, the reflectance in the stop band approaches 100%.

A wavelength within the target wavelength range W will be defined as λ, the refractive index of the first refractive-index layers 24a will be defined as n_H, and the refractive index of the second refractive-index layers 24b will be defined as n_L. A DBR including one or more pair layers of first refractive-index layers 24a having a thickness of λ/(4n_H) and second refractive-index layers 24b having a thickness of λ/(4 n_L) efficiently reflects light with the wavelength λ. If the target wavelength range W is a range greater than or equal to a wavelength λ_i and less than or equal to a wavelength λ_f, the DBR can include a pair layer corresponding to the wavelength λ_i to a pair layer corresponding to the wavelength by varying the thicknesses of the first refractive-index layers 24a and the second refractive-index layers 24b in a stepwise fashion. As a result, the DBR can efficiently reflect all the light within the target wavelength range W.

The DBR may be composed of, for example, a material with low absorbance with respect to light within the target wavelength range W. If the target wavelength range W is within the visible-light region, the material may be at least one selected from the group consisting of SiO₂, Al₂O₃, SiO_xN_y, Si₃N₄, Ta₂O₅, and TiO₂. If the target wavelength range W is within the infrared region, the material may be at least one selected from the group consisting of monocrystalline Si, polycrystalline Si, and amorphous Si, in addition to SiO₂, Al₂O₃, SiO_xN_y, Si₃N₄, Ta₂O₅, and TiO₂ mentioned above.

The interference layer 26 has a lower surface 26s₁ in contact with the reflective layer 24 and also has an upper surface 26s₂ at the opposite side thereof. In the filter 100 illustrated in FIG. 11A, the lower surface 26s₁ corresponds to a first surface, and the upper surface 26s₂ corresponds to a second surface. In the example illustrated in FIG. 11A, the upper surface 26s₂ is exposed to the outside and is in contact with the air. A transparent layer may be further stacked on the interference layer 26. In this case, the upper surface 26s₂ is in contact with the transparent layer. The reflectance (referred to as “first reflectance” hereinafter) of the lower surface 26s₁ with respect to light in the target wavelength range W may be, for example, higher than or equal to 80%. The first reflectance may be lower than 80%, but may be designed to be higher than or equal to 40% from the standpoint of suppressing reflection. The reflectance (referred to as “second reflectance” hereinafter) of the upper surface 26s₂ with respect to light in the target wavelength range W is lower than the first reflectance and may be, for example, higher than or equal to 1% and lower than 30%. There is a fixed difference of 10% or more between the first reflectance and the second reflectance.

On the other hand, in the filters 100 of the light detection device 300 illustrated in FIG. 10B, the reflective layer 24 is disposed over the upper surface of the interference layer 26. In the filters 100 of the light detection device 300 illustrated in FIG. 10B, the upper surface of the interference layer 26 corresponds to the first surface, and the lower surface corresponds to the second surface.

In this description, unless an accurate position of a surface that reflects light becomes a problem, the light within the interference layer 26 is reflected at the lower surface 26s₁ and the upper surface 26s₂. In this embodiment, a portion of light incident on the reflective layer 24 from the interference layer 26 actually enters the reflective layer 24 so as to be reflected at the interfaces between the first refractive-index layers 24a and the second refractive-index layers 24b. The interfaces where the light is reflected vary depending on the wavelength. However, for the sake of convenience, these beams of light are treated as being reflected at the lower surface 26s₁.

The reflection of the light at the lower surface 26s₁ and the upper surface 26s₂ causes standing waves to be formed within the interference layer 26. As a result, if the thickness of the interference layer 26 is greater than or equal to a predetermined value, the transmission spectrum of each filter 100 has maximum transmittance values at various wavelengths in the target wavelength range W. In other words, the transmission spectrum of the filter 100 has peaks within the target wavelength range W. In this description, such a filter will be referred to as “multimode filter”. If the DBR includes a pair layer corresponding to the wavelength λ, the thickness of the interference layer 26 that can realize a multimode filter may be, for example, twice the thickness of the first refractive-index layers 24a, that is, greater than or equal to λ/(2n_H). A multimode filter may be realized by appropriately designing the refractive index of the interference layer 26 instead of the thickness of the interference layer 26. Alternatively, a multimode filter may be realized by appropriately designing both the refractive index and the thickness of the interference layer 26.

The interference layer 26 may be composed of a material similar to that of the DBR. The interference layer 26 is not limited to a single layer and may include stacked layers. Such layers may be composed of different materials. The layers may have different refractive indices to an extent that they do not have a substantial effect on the transmission spectrum of each filter 100. Reflection may occur at the interfaces between layers with different refractive indices. However, the layers may be regarded as a substantially uniform part of the interference layer 26 so long as they do not have a substantial effect on the transmission spectrum. A permissible relative error in the refractive indices is greater than or equal to 0% and less than or equal to 9%. The relative error is a value obtained by dividing an absolute value of a difference between a maximum refractive index and a minimum refractive index by the maximum refractive index. For example, the refractive indices in the visible-light regions of Ta₂O₅ and Si₃N₄ are 2.2 and 2.05, respectively. The relative error in these refractive indices is about 7%. Therefore, the stacked Ta₂O₅ and Si₃Na layers may be regarded as a substantially uniform part of the interference layer 26.

In the following description, the structure illustrated in FIG. 11A will be referred to as “single-sided DBR structure”. In addition to the structure illustrated in FIG. 11A, a structure having a reflective layer 24 additionally stacked on the interference layer 26 will be referred to as “double-sided DBR structure”. In the single-sided DBR structure, the reflective layer 24 is provided on one of the lower surface 26s₁ and the upper surface 26s₂ of the interference layer 26, but is not provided on the other surface. In the double-sided DBR structure, reflective layers are provided on both the lower surface 26s₁ and the upper surface 26s₂ of the interference layer 26.

Next, an example of transmission spectra of the filters 100 will be described with reference to FIG. 11B. FIG. 11B illustrates an example of light transmission spectra of the single-sided DBR structure and the double-sided DBR structure when light vertically enters the structures. In the example illustrated in FIG. 11B, the target wavelength range W is greater than or equal to 450 nm and less than or equal to 850 nm. A solid line illustrated in FIG. 11B indicates the transmission spectrum of the single-sided DBR structure. A dashed line in FIG. 11B indicates the transmission spectrum of the double-sided DBR structure. As illustrated in FIG. 11B, multimode filters can be obtained from both the single-sided DBR structure and the double-sided DBR structure. However, the characteristics of the multimode filters of the two structures are different from each other with respect to the following points. The transmission spectrum of the single-sided DBR structure has wide peaks and has maximum transmittance of about 0.5 and minimum transmittance of about 0.1. In other words, the contrast ratio of the transmittance is low. In contrast, the transmission spectrum of the double-sided DBR structure has sharp peaks and has maximum transmittance of about 1.0 and minimum transmittance of about 0.02. In other words, the contrast ratio of the transmittance is high.

In the single-sided DBR structure, the base line of the transmittance rises, as compared with the double-sided DBR structure. In this example, the average transmittance within the target wavelength range W in the single-sided DBR structure is approximately 0.26, and the average transmittance within the target wavelength range W in the double-sided DBR structure is approximately 0.1. In the single-sided DBR structure, the average transmittance is about twice that in the double-sided DBR structure. Accordingly, the single-sided DBR structure can suppress a loss in light intensity during an imaging process.

In the example illustrated in FIG. 11B, in the single-sided DBR structure and the double-sided DBR structure, M_i=0.1 and M_i=−0.14, respectively, with respect to each of the wavelength bands. If each of the filters 100 included in the filter array 10 includes the single-sided DBR structure, M_i≥0.1 can be satisfied with respect to each wavelength band.

Next, an example of a specific structure of the filter array 10 according to this embodiment that satisfies M_i≥0.1 with respect to each of the wavelength bands will be described with reference to FIGS. 12A and 12B. FIGS. 12A and 12B are cross-sectional views schematically illustrating a third example and a fourth example, respectively, of the light detection device 300. The third example and the fourth example are different from the first example and the second example in that a reflective layer 25 includes a metallic film instead of a DBR. The reflectance of the metallic film in the target wavelength range W is dependent on the material of the metallic film. An absorption coefficient of the metallic film in the target wavelength range W is dependent on the thickness of the metallic film.

The metallic film may be composed of a material whose reflectance in the target wavelength range W is higher than or equal to 90%. If the target wavelength range W is within the visible-light region, the material of the metallic film with the reflectance being higher than or equal to 90% may be at least one selected from the group consisting of Ag and Al. If the target wavelength range W is within the infrared region, the material of the metallic film with the reflectance being higher than or equal to 90% may be at least one selected from the group consisting of Ag, Al, Au, and Cu. Even if the metallic film has relatively low reflectance, the metallic film is still useful in that the reflectance is suppressed. For example, the metallic film may be composed of a material whose reflectance in the target wavelength range W is higher than or equal to 40% and lower than or equal to 70%. If the target wavelength range W is within the visible-light region or the infrared region, the material of the metallic film with the reflectance being higher than or equal to 40% and lower than or equal to 70% may be at least one selected from the group consisting of Ni and Pt. The metallic film may be composed of an alloy. The metallic film may be provided by plating.

The thickness of the metallic film may be, for example, larger than or equal to 1 nm and smaller than or equal to 100 nm. In this case, the transmittance of the metallic film from the visible-light region to the infrared region may relatively increase. As a result, light in the visible light region to the near-infrared region can be effectively transmitted through the metallic film. The thickness of the metallic film may be smaller than or equal to several tens of nm.

In the examples illustrated in FIGS. 10A and 10B and FIGS. 12A and 12B, the reflective layer exists only at one side of the interference layer 26. If the first reflectance and the second reflectance of the interference layer 26 have a fixed difference, as described above, reflective layers may exist at both sides of the interference layer 26.

Next, another example of the specific structure of the filter array 10 according to this embodiment that satisfies M_i≥0.1 with respect to each of the wavelength bands will be described with reference to FIGS. 13A and 13B.

FIG. 13A is a perspective view schematically illustrating a fifth example of the light detection device 300. In the example illustrated in FIG. 13A, the filter array 10 includes filters 110. Each of the filters 110 is a sub filter array in which sub filters 30 are arranged. The filter array 10 is disposed such that light transmitted through the filters 110 enters each of the light detection elements 60a in the image sensor 60. In the example illustrated in FIG. 13A, one light detection element 60a detects light transmitted through 4×4 sub filters 30. Not all of the filters have to be sub filter arrays. The filter array according to this embodiment may include at least one sub filter array.

FIG. 13B is a perspective view schematically illustrating an example of each filter 110 serving as a sub filter array and the corresponding light detection element 60a. The sub filters 30 include various types of first sub filters 30a with different transmission wavelength ranges, and also include at least one second sub filter 30b that transmits light in each wavelength band. In the example illustrated in FIG. 13B, a hatched sub filter indicates a first sub filter 30a, and a white sub filter indicates a second sub filter 30b. The number of first sub filters 30a and the number of second sub filters 30b vary for each filter 110 serving as a sub filter array. The filters 110 serving as sub filter arrays have different transmission spectra.

The various types of first sub filters 30a may include, for example, RGB color filters, namely, a red filter, a green filter, and a blue filter. In place of the RGB color filters or in addition to the RGB filters, the various types of first sub filters 30a may include at least one of CMY filters, namely, a cyan filter, a magenta filter, and a yellow filter. The second sub filter 30b may be, for example, a transparent filter having high transmittance in the visible-light region. In place of the second sub filter 30b, an opening may be provided. The baseline for the transmittance of the filter 110 illustrated in FIG. 13B can be increased by the second sub filter 30b or the opening. As a result, the filter array 10 illustrated in FIG. 13A can satisfy M_i>0.1 with respect to each of the wavelength bands. Such a filter array 10 has noise immunity. The percentage of an area of the second sub filter 30b or the opening occupying the total area of each filter 110 serving as a sub filter array is higher than or equal to 4%. The percentage of 4% corresponds to a case where, for example, 5×5 sub filters 30 include one second sub filter 30b.

Next, an example of transmission spectra of the filters 110 serving as sub filter arrays will be described with reference to FIG. 14. FIG. 14 illustrates the transmission spectra of eight types of sub filter arrays. The 4×4 sub filters 30 in each filter 110 serving as a sub filter array includes 14 first sub filters 30a having three types of RGB color filters arranged therein and two second sub filters 30b that transmit white light. The percentage of an area of the second sub filters 30b occupying the total area of the filter 110 serving as a sub filter array is 12.5%. With the second sub filters 30b, the minimum transmittance in the transmission spectra of all the sub filter arrays is higher than or equal to 0.15. As a result, M_i is equal to about 0.18 with respect to each of the wavelength bands, so that M_i>0.1 is satisfied. In contrast, if all the 4×4 sub filters 30 in each sub filter array are first sub filters 30a, M_i is equal to about 0.05 with respect to each of the wavelength bands, so that M_i>0.1 is not satisfied.

If M_i is too large, the sub filters 30 may partially include an ND filter, so that the minimum transmittance value of each filter 110 serving as a sub filter array can be reduced. As a result, the value of M_i decreases.

INDUSTRIAL APPLICABILITY

The light detection system and the filter array according to the present disclosure may be used in, for example, a camera and a measurement device that acquire a multi-wavelength two-dimensional image. The light detection system and the filter array according to the present disclosure are also applicable to, for example, biological, medical, or cosmetic-oriented sensing, a system for inspecting foreign matter and residual pesticides in food, a remote sensing system, and a vehicular sensing system.

Claims

1. A filter array used in a light detection device that generates image data corresponding to each of N wavelength bands included in a specific wavelength range, N being an integer greater than or equal to 2, the filter array comprising: optical filters,wherein the optical filters include optical filters with different light transmittance with respect to each of the N wavelength bands, andwherein Mi≥0.1 with respect to each of the N wavelength bands,where Mi=μi−σi, μi denoting an average value of light transmittance of the optical filters with respect to light having a wavelength included in an i-th wavelength band of the N wavelength bands, i being an integer greater than or equal to 1 and less than or equal to N, σi denoting a standard deviation of the light transmittance of the optical filters with respect to the light having the wavelength included in the i-th wavelength band.

2. The filter array according to claim 1, wherein σi≥0.05 with respect to each of the N wavelength bands.

3. The filter array according to claim 1, wherein μi≥0.2 with respect to each of the N wavelength bands.

4. The filter array according to claim 1, wherein Mmax/Mmin≤3,where Mmax and Mmin denote a maximum Mi and a minimum Mi, respectively, with respect to the N wavelength bands.

5. The filter array according to claim 1, wherein at least one optical filter of the optical filters includes an interference layer having a first surface and a second surface opposite the first surface, anda reflective layer provided on the first surface,wherein a transmission spectrum of the at least one optical filter has maximum values in the specific wavelength range, andwherein the reflective layer is not provided on the second surface.

6. The filter array according to claim 5, wherein the reflective layer includes at least one selected from the group consisting of a distributed Bragg reflector and a metallic film.

7. The filter array according to claim 6, wherein the distributed Bragg reflector includes at least one set of a first refractive-index layer and a second refractive-index layer, andwherein a refractive index of the first refractive-index layer is higher than a refractive index of the second refractive-index layer.

8. The filter array according to claim 7, wherein the first refractive-index layer has a thickness of λ/(4nH), and the second refractive-index layer has a thickness of λ(4 nL), andwherein the interference layer has a thickness larger than λ/(2nH),where λ denotes a wavelength included in the specific wavelength range, nH denotes the refractive index of the first refractive-index layer, and nL denotes the refractive index of the second refractive-index layer.

9. The filter array according to claim 6, wherein the metallic film has a thickness larger than or equal to 1 nm and smaller than or equal to 100 nm.

10. The filter array according to claim 1, wherein the light detection device includes an image sensor,wherein the filter array is disposed such that light transmitted through the optical filters enters the image sensor,wherein at least one of the optical filters is a sub filter array including two-dimensionally-arranged sub filters,wherein the sub filter array includes first sub filters having different transmission wavelength ranges and one or more second sub filters or openings each transmitting N light beams having a wavelength included in a corresponding wavelength band of the N wavelength bands, andwherein a percentage of an area of the one or more second sub filters or openings occupying a total area of the sub filter array is higher than or equal to 4%.

11. The filter array according to claim 10, wherein the first sub filters include a red filter, a green filter, and a blue filter.

12. A light detection system comprising: the filter array according to claim 1; andan image sensor that is disposed at a position where the image sensor receives light transmitted through the optical filters and that has sensitivity to light having a wavelength included in the specific wavelength range.

13. The light detection system according to claim 12, further comprising: a processing circuit that generates the image data based on data indicating a spatial distribution of the light transmittance of the optical filters and compressed image data acquired by the image sensor.