The present disclosure relates to an optical filter array, a photodetection device, and a photodetection system.
Utilization of spectral information on a large number of bands, e.g. several tens of bands, each of which is a narrow band makes it possible to understand in detail the physical properties of a physical object, although doing so has been impossible with a conventional RGB image. A cameral that acquires such multiwavelength information is called “hyperspectral camera”. Hyperspectral cameras have been utilized in various fields such as food inspection, biopsies, drug development, and componential analyses of minerals.
U.S. Patent Application Publication No. 2016/138975 and Japanese Unexamined Patent Application Publication No. 2016-100703 disclose hyperspectral cameras utilizing compressed sensing. For example, U.S. Patent Application Publication No. 2016/138975 discloses an imaging device including an encoding element that is an array of a plurality of optical filters differing in wavelength dependence of light transmittance from each other and an image sensor that detects light having passed through the encoding element. The image sensor acquires one multiple-wavelength image by simultaneously detecting light in a plurality of wavelength bands for each pixel. By applying compressed sensing to the multiple-wavelength image thus acquired, images are reconstructed separately for each of the plurality of wavelength bands.
In one general aspect, the techniques disclosed here feature an optical filter array that is used in a photodetection device generating image data separately for each of N wavelength bands, N being an integer greater than or equal to 4. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that μi is an average of transmittances of the plurality of optical filters for light in an ith wavelength band of the N wavelength bands, i being an integer greater than or equal to 1 and less than or equal to N, a standard deviation σμ of the average μi of the transmittances for the N wavelength bands is expressed as
and the standard deviation σμ of the average μi of the transmittances is less than or equal to 0.13.
In another general aspect, the techniques disclosed here feature an optical filter array that is used in a photodetection device generating image data separately for each of N wavelength bands, N being an integer greater than or equal to 4. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that σi is a standard deviation of transmittances of the plurality of optical filters for light in an ith wavelength band of the N wavelength bands, i being an integer greater than or equal to 1 and less than or equal to N, an average of standard deviations σi of the transmittances for the N wavelength bands is greater than or equal to 0.07.
In still another general aspect, the techniques disclosed here feature an optical filter array that is used in a photodetection device generating image data separately for each of N wavelength bands, N being an integer greater than or equal to 4. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that μi is an average of transmittances of the plurality of optical filters for light in an ith wavelength band of the N wavelength bands, i being an integer greater than or equal to 1 and less than or equal to N, that σi is a standard deviation of the transmittances of the plurality of optical filters for the light in the ith wavelength band, and that Ri=(μi+3σi)/(μi−3σi), an average of Ri for the N wavelength bands is greater than or equal to 2.0.
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.
Prior to a description of an embodiment of the present disclosure, underlying knowledge found by the inventors is described.
In a hyperspectral camera utilizing compressed sensing, the quality of images to be reconstructed depends on the optical properties of an encoding element, i.e. an optical filter array. In a case where the characteristics of the optical filter array are not appropriate, there are great errors in images to be restored, with the result that high-quality reconstructed images cannot be obtained. Mathematically, an ideal optical filter array that performs spatially and spectrally (i.e. in frequency or wavelength space) random sampling is desirable. However, it is difficult to actually fabricate such an ideally random optical filter array. That is, there has been room for improvement in a specific configuration of an optical filter array capable of reducing errors entailed by reconstruction of images of a plurality of wavelength bands.
The following gives a brief overview of an embodiment of the present disclosure.
Thought is given here to a histogram of the transmittances of the plurality of optical filters of the filter array 10 for the ith (where i is an integer greater than or equal to 1 and less than or equal to N) wavelength band.
The histogram can be obtained by measuring the transmittance of each of the optical filters of the filter array 10 with a photodetector that detects light intensity with a predetermined number of tones. For example, the histogram can be obtained by using a photodetector, such as an image sensor, that can detect a two-dimensional distribution of light intensity with a predetermined number of tones such as eight bits or sixteen bits. Specifically, the transmittance of light in the ith wavelength band of each of the filters of the filter array 10 can be calculated from the ratio of the intensity of light in the ith wavelength band as detected with the filter array 10 placed to the intensity of light in the ith wavelength band as detected with no filter array 10 placed. A histogram such as that illustrated in
For example, each of the filters of the filter array 10 can be constituted using a multi-layer film, an organic material, a diffraction grating structure, or a metal-containing fine structure.
A case is described here as an example where each of the filters of the filter array 10 is constituted by a Fabry-Perot filter (hereinafter referred to as “FP filter”). The FP filter includes a first reflective layer, a second reflective layer, and an intermediate layer sandwiched between the first reflective layer and the second reflective layer. Each of the reflective layers may be formed from either a dielectric multi-layer film or a metal thin film. The intermediate layer has a thickness and a refractive index by which a resonant structure having at least one resonant mode is formed. The resonant structure is high in transmittance of light of a wavelength corresponding to the resonant mode and low in transmittance of light of another wavelength. Different transmission spectra can be achieved for each separate filter by varying the refractive index or thickness of the intermediate layer from one filter to another.
According to the study conducted by the inventors, great variations in the average and standard deviation of the transmittance of a filter array lead to a decrease in reproducibility of images and a deterioration in convergence of restoring operations. Further, it was found that there is also a decrease in reproducibility of images in a case where the average of standard deviations of transmittance for each band is too small.
The inventors found the foregoing problems and studied a configuration of a filter array for solving these problems. According to an embodiment of the present disclosure, a filter array is designed so that the standard deviation (or variance) of the average transmittance in all bands is greater than or equal to a particular value. According to another embodiment, a filter array is designed so that the average of standard deviations of transmittance for each band is greater than or equal to a particular value. Such a design makes it possible to reduce restoration errors in images for each band.
An optical filter array according to an embodiment of the present disclosure is used in a photodetection device that generates image data separately for each of N (where N is an integer greater than or equal to 4) wavelength bands. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that μi is an average of transmittances of the plurality of optical filters for light in an ith wavelength band (where i is an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, a standard deviation σμ of the average p of the transmittances for the N wavelength bands is expressed as
and the standard deviation σμ of the average μi of the transmittances is less than or equal to 0.13.
According to the foregoing configuration, each of the optical filters is designed so that the standard deviation σμ of the average μi of the transmittances for the N wavelength bands takes on a comparatively small value less than or equal to 0.13. This makes it possible to enhance the uniformity of the average transmittance of the optical filter array for each wavelength band. This can result in reduced errors in images in each separate wavelength band that are generated, for example, by a process that involves the use of compressed sensing.
An optical filter array according to another embodiment of the present disclosure is used in a photodetection device that generates image data separately for each of N (where N is an integer greater than or equal to 4) wavelength bands. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that σi is a standard deviation of transmittances of the plurality of optical filters for light in an ith wavelength band (where i is an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, an average of standard deviations σi of the transmittances for the N wavelength bands is greater than or equal to 0.07.
According to the foregoing configuration, each of the optical filters is designed so that the average of the standard deviations σi of the transmittances for the N wavelength bands takes on a comparatively large value greater than or equal to 0.07. This makes it possible to improve the dispersibility of the transmittance of the optical filter array for each wavelength band. This can result in reduced errors in images in each separate wavelength band that are generated, for example, by a process that involves the use of compressed sensing.
An optical filter array according to still another aspect of the present disclosure is used in a photodetection device that generates image data separately for each of N (where N is an integer greater than or equal to 4) wavelength bands. The optical filter array includes a plurality of optical filters. The plurality of optical filters include plural types of optical filters differing in transmittance from each other in each of the N wavelength bands. Assuming that μi is an average of transmittances of the plurality of optical filters for light in an ith wavelength band (where i is an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, that σi is a standard deviation of the transmittances of the plurality of optical filters for the light in the ith wavelength band, and that Ri=(μi+3σi)/(μi−3σi), an average of Ri for the N wavelength bands is greater than or equal to 2.0.
According to the foregoing configuration, each of the optical filters is designed so that the average of Ri takes on a comparatively large value greater than or equal to 2.0. This makes it possible to improve the dispersibility of the transmittance of the optical filter array for each wavelength band. This can result in reduced errors in images in each separate wavelength band that are generated, for example, by a process that involves the use of compressed sensing.
In an embodiment, a transmittance of a peak in a histogram of the transmittances as obtained by measuring a transmittance of each of the plurality of optical filters for the light in the ith wavelength band with a photodetector that detects light intensity with a predetermined number of tones may be smaller than the average μi of the transmittances of the plurality of optical filters for the light in the ith wavelength band.
At least one of the plurality of optical filters may be a Fabry-Perot filter. The Fabry-Perot filter can be fabricated more easily than another type of filter formed, for example, from an organic material.
At least one of the plurality of filters may include a first reflective layer, a second reflective layer, and an intermediate layer between the first reflective layer and the second reflective layer and may include a resonant structure having a plurality of resonant modes differing in order from each other. Such a structure makes it possible to achieve a filter with a high transmittance for a plurality of wavelengths.
A center wavelength λi in the ith wavelength band and the average μi of the transmittances of the plurality of optical filters for the light in the ith wavelength band may have a positive correlation. In a case where each optical filter is the aforementioned Fabry-Perot filter, such a characteristic can be typically obtained.
A photodetection device according to still another embodiment of the present disclosure includes the optical filter array according to any of the above and an image sensor that detects light having passed through the optical filter array.
A photodetection system according to still another embodiment of the present disclosure includes the photodetection device and a signal processing circuit that generates image data for each of the N wavelength bands in accordance with a signal outputted from the image sensor.
In the present disclosure, all or some of the circuits, units, devices, members, or sections or all or some of the functional blocks in the block diagrams may be implemented as one or more of electronic circuits including, but not limited to, a semiconductor device, a semiconductor integrated circuit (IC), or an LSI (large scale integration). The LSI or IC can be integrated into one chip, or also can be a combination of multiple chips. For example, functional blocks other than a memory may be integrated into one chip. The name used here is LSI or IC, but it may also be called system LSI, VLSI (very large scale integration), or ULSI (ultra large scale integration) depending on the degree of integration. A Field Programmable Gate Array (FPGA) that can be programmed after manufacturing an LSI or a reconfigurable logic device that allows reconfiguration of the connection or setup of circuit cells inside the LSI can be used for the same purpose.
Further, it is also possible that all or some of the functions or operations of the circuits, units, devices, members, or sections are implemented by executing software. In such a case, the software is recorded on one or more non-transitory recording media such as a ROM, an optical disk, or a hard disk drive, and when the software is executed by a processor, the software causes the processor together with peripheral devices to execute the functions specified in the software. A system or device may include such one or more non-transitory recording media on which the software is recorded and a processor together with necessary hardware devices such as an interface.
The following describes a more specific embodiment of the present disclosure. Note, however, that an unnecessarily detailed description may be omitted. For example, a detailed description of a matter that is already well known and a repeated description of substantially identical configurations may be omitted. This is intended to avoid unnecessary redundancy of the following description and facilitate understanding of persons skilled in the art. It should be noted that the inventors provide the accompanying drawings and the following description for persons skilled in the art to fully understand the present disclosure and do not intend to thereby limit the subject matter recited in the claims. In the following description, identical or similar constituent elements are given the same reference signs. A signal representing an image (i.e. a set of signals representing the pixel values of each separate pixel) is herein sometimes simply referred to as “image”. The following description involves the use of an xyz coordinate shown in the drawings.
The filter array 10 includes a plurality of translucent areas arranged in rows and columns. The filter array 10 is an optical element in which the transmission spectrum of light, i.e. the wavelength dependence of light transmittance, varies from one area to another. The filter array 10 allows passage of the incident light by modulating the intensity of the incident light. A configuration of the filter array 10 will be described in detail later.
The filter array 10 may be disposed near or directly above the image sensor 60. The term “near” here means that the filter array 10 is so close to the image sensor 60 that an image of light from the optical system 40 is formed on a surface of the filter array 10 with a certain degree of definition. The term “directly above” here means that the filter array 10 is so close to the image sensor 60 that almost no gap is formed between them. The filter array 10 and the image sensor 60 may be integrated. A device including the filter array 10 and the image sensor 60 is referred to as “photodetection device 300”.
The filter array 10 may be placed at a distance from the image sensor 60.
The optical system 40 includes at least one lens. Although
The image sensor 60 is a monochromatic photodetector having a plurality of photodetection elements (herein also referred to as “pixels”) arranged in a two-dimensional array. The image sensor 60 may for example be a CCD (charge-coupled device), a CMOS (complementary metal oxide semiconductor), an infrared array sensor, a terahertz array sensor, or a millimeter wave array sensor. The photodetection elements include, for example, photodiodes. The image sensor 60 does not necessarily need to be a monochromatic sensor. The image sensor 60 may for example be a color sensor having a R/G/B, R/G/B/IR, or R/G/B/W filter. Using a color sensor makes it possible to increase the amount of information regarding wavelengths and improve the accuracy of reconstruction of spectroscopic separate images. However, since the use of a color sensor leads to a decrease in the amount of information in spatial directions (x and y directions), there is a trade-off between the amount of information regarding wavelengths and resolution The range of wavelengths to be acquired may be arbitrarily determined, and may be a range of ultraviolet, near-infrared, mid-infrared, far-infrared, microwave, or microwave or radio wave wavelengths without being limited to a range of visible wavelengths.
On the basis of an image 120 acquired by the image sensor 60, the signal processing circuit 200 reconstructs a plurality of separate images 220W1, 220W2, 220W3, . . . , and 220WN containing multiwavelength information. The plurality of separate images 220W1, 220W2, 220W3, . . . , and 220WN and a method by which the signal processing circuit 200 processes an image signal will be described in detail later. The signal processing circuit 200 may be incorporated into the photodetection device 300, or may be a constituent element of a signal processing device electrically connected to the photodetection device 300 by wire or radio.
The following describes the filter array 10 according to the present embodiment. The filter array 10 is disposed on the optical path of incident light from the physical object 70, modulates the intensity of the incident light for each wavelength, and outputs the resulting light. This process, which is done by the filter array 10, is herein referred to as “encoding”.
In the example shown in
In the example shown in
As noted above, the light transmittance of each of the areas varies from one wavelength to another. Accordingly, the filter array 10 transmits much of a component of the incident light lying within a certain wavelength region and does not transmit as much of a component of the incident light lying within another wavelength region. For example, the transmittance of light in k out of the N wavelength bands may be higher than 0.5, and the transmittance of light in the remaining N-k wavelength regions may be lower than 0.5. k is an integer that satisfies 2≤k<N. If the incident light is white light containing all wavelength components of visible light evenly, the filter array 10 modulates the incident light for each area into light having a plurality of wavelength-discrete peaks of intensity, and outputs these multiwavelength lights superimposed on each other.
In a case where the filter array 10 is disposed near or directly above the photodetector, the plurality of areas of the filter array 10 may be placed at spacings, called cell pitches, that are substantially equal to pitches at which pixels of the photodetector are placed. In this way, the resolution of an encoded image of light emitted from the filter array 10 is substantially equal to the resolution of the pixels. The after-mentioned operation can be facilitated by allowing light having passed through a cell to fall on only one pixel. In a case where the filter array 10 is placed at a distance from the photodetector, the cell pitches may be made finer according to the distance.
The examples shown in
Some of all cells, e.g. half of the cells, may be replaced by transparent areas. Such a transparent area transmits, at about equally high transmittances, e.g. at a transmittances higher than or equal to 80%, light in all of the wavelength regions W1 to WN included in the target wavelength region. In such a configuration, the plurality of transparent areas may be arranged, for example, in a checkered pattern. That is, in two array directions of the plurality of areas of the filter array 10, the areas whose light transmittances vary according to wavelength and the transparent areas may be alternately arrayed.
The following describes an example of a process that is performed by the signal processing circuit 200. The signal processing circuit 200 reconstructs the multiwavelength separate images 220 on the basis of the image 120 outputted from the image sensor 60 and the spatial distribution characteristics of transmittance of the filter array 10 for each wavelength. The term “multiwavelength” here means a larger number of wavelength regions than the number of wavelength regions of three colors of RGB acquired, for example, by an ordinary color camera. This number of wavelength regions may be a number ranging, for example, approximately from 4 to 100. This number of wavelength regions is referred to as “number of bands”. In some applications, the number of bands may exceed 100.
Desired data is the separate images 220, and the data is denoted by f. When the number of spectral bands is denoted by N, f is data obtained by integrating image data f1, f2, . . . , and fN of each separate band. When the number of pixels in an x direction of the image data to be obtained is denoted by n and the number of pixels in a y direction is denoted by m, each of the image data f1, f2, . . . , and fN is a set of two-dimensional data representing n×m pixels. Accordingly, the data f is three-dimensional data representing the number of elements n×m×N. Meanwhile, the number of elements of data g representing the image 120 acquired though encoding and multiplexing by the filter array 10 is n×m. In the present embodiment, the data g can be expressed by Formula (1) as follows:
In this formula, f1, f2, . . . , and fN are data having n×m elements. Accordingly, the right-hand vector is technically a one-dimensional vector with an n×m×N rows and one column. The vector g is expressed and calculated in terms of a one-dimensional vector with an n×m rows and one column. The matrix H represents a transformation by which the components f1, f2, . . . , and fN of the vector f are subjected to encoding and intensity modulation with different pieces of encoding information for each wavelength band and added together. Accordingly, H is a matrix with n×m rows and n×m×N columns. The matrix H is herein sometimes referred to as “system matrix”.
It now seems that once the vector g and the matrix H are given, f can be computed by solving an inverse problem of Formula (1). However, since the number of elements n×m×N of the data f to be obtained is larger than the number of elements n×m of the acquired data g, this problem is an ill-posed problem that cannot be directly solved. To address this problem, the signal processing circuit 200 of the present embodiment obtains the solution using a technique of compressed sensing through the use of redundancy of images contained in the data f. Specifically, the data f to be obtained is estimated by solving Formula (2) as follows:
In this formula, f′ represents the data f thus estimated. The first term in parentheses of the above formula represents a difference between an estimated result Hf and the acquired data g, i.e. a so-called residual. Although the residual is a sum of squares here, the residual may for example be an absolute value or a square root of sum of squares. The second term in parentheses is the after-mentioned regularization term or stabilization term. Formula (2) means obtaining f that minimizes the sum of the first term and the second term. The signal processing circuit 200 can compute the final solution f′ through convergence of solutions by a recursive iterative operation.
The first term in parentheses of Formula (2) means an operation of finding the sum of squares of the difference between the acquired data g and Hf obtained by a system transformation by the matrix H of f being estimated. Φ(f) of the second term is a constraint on the regularization of f, and is a function reflecting sparse information of the estimated data. Φ(f) functions to bring about an effect of smoothing or stabilizing the estimated data. The regularization term may be expressed, for example, by a discrete cosine transformation (DCT), a wavelet transformation, a Fourier transformation, or a total variation (TV) of f. For example, in a case where a total variation is used, stable estimated data can be acquired with a reduction in the effect of noise of the observed data g. The sparsity of the physical object 70 in a space of each regularization term varies depending on the texture of the physical object 70. It is possible to choose a regularization term having a space in which the texture of the physical object 70 becomes sparser. Alternatively, it is possible to incorporate a plurality of regularization terms into the operation. τ is a weighting factor. A greater weighting factor τ leads to an increase in reduction of redundant data, and by extension to a higher rate of compression. A smaller weighting factor τ leads to a weaker convergence to the solution. The weighting factor τ is set to such an appropriate value that f converges to some extent and does not become overcompressed.
Although, in this example operation, the compressed sensing shown in Formula (2) is used, another method may be used to obtain the solution. For example, another statistical method such as maximum likelihood estimation or a Bayesian estimation method may be used. Further, the number of separate images 220 is arbitrary, and each of the wavelength bands may be arbitrarily set. Details of the reconstruction method are disclosed in U.S. Patent Application Publication No. 2016/138975. The entire contents of the disclosure in U.S. Patent Application Publication No. 2016/138975 are hereby incorporated by reference.
The following describes a specific example configuration of the filter array 10 that reduces errors in images to be reconstructed.
The following description assumes that each of the filters of the filter array 10 is a Fabry-Perot (FP) filter. The FP filter includes a first reflective layer, a second reflective layer, and an intermediate layer sandwiched between the first reflective layer and the second reflective layer. Each of the reflective layers may be formed from either a dielectric multi-layer film or a metal thin film. The intermediate layer has a thickness and a refractive index by which a resonant structure having at least one resonant mode is formed. The transmittance of light of a wavelength corresponding to the resonant mode is high, and the transmittance of light of another wavelength is low. Different transmission spectra can be achieved for each separate filter by varying the refractive index or thickness of the intermediate layer from one filter to another.
The image sensor 60 includes a plurality of photodetection elements 60a. Each of the plurality of photodetection elements 60a is disposed to face one of the plurality of filters 100. Each of the plurality of photodetection elements 60a has sensitivity to light in a particular wavelength region. The particular wavelength region corresponds to the aforementioned target wavelength region W. The phrase “having sensitivity to light in a certain wavelength region” herein refers to having substantive sensitivity needed to detected light in the wavelength region. For example, the phrase refers to having an external quantum efficiency of 1% or higher in the wavelength region. The external quantum efficiency of a photodetection element 60a may be higher than or equal to 10%. The external quantum efficiency of a photodetection element 60a may be higher than or equal to 20%. All of the plurality of wavelengths at which the light transmittance of each of the filters 100 assumes local maximum values are included in the target wavelength region W.
A filter 100 including the aforementioned resonant structure is herein referred to as “Fabry-Perot filter”. A portion of a transmission spectrum that has a local maximum value is herein referred to as “peak”, and a wavelength at which a transmission spectrum has a local maximum value is herein referred to as “peak wavelength”.
Let it be assumed in a filter 100 that L is the thickness of the intermediate layer 26, n is the refractive index of the intermediate layer 26, θi is the angle of incidence of light arriving at the filter 100, and m is the mode number of a resonant mode. m is an integer greater than or equal to 1. In this case, the peak wavelength λm of the transmission spectrum of the filter 100 is expressed by Formula (3) as follows:
Let it be assumed that λi and λe are the shortest and longest wavelengths, respectively, in the target wavelength region W. A filter 100 in which there is one m that satisfies λi≤λm≤λe is herein referred to as “single-mode filter”. A filter 100 in which there are two or more m's that satisfy λi≤λm≤λe is herein referred to as “multimode filter”. The following describes an example of a case where the shortest and longest wavelengths λi and λe in the target wavelength region W are equal to 400 nm and 700 nm, respectively.
For example, in the case of a filter 100 in which the thickness L is equal to 300 nm, the refractive index n is equal to 1.0, and the vertical incidence θi is equal to 0 degree, the peak wavelength λ1 at the time that m=1 is equal to 600 nm, and the peak wavelength λm≥2 at the time that m≥2 is shorter than or equal to 300 nm. Accordingly, this filter 100 is a single-mode filter having one peak wavelength in the target wavelength region W.
Meanwhile, when the thickness L is greater than 300 nm, a plurality of peak wavelengths are included in the target wavelength region W. For example, in the case of a filter 100 in which the thickness L is equal to 3000 nm, the refractive index n is equal to 1.0, and the vertical incidence θi is equal to 0 degree, the peak wavelength λ1≤m≤8 at the time that 1≤m≤8 is longer than or equal to 750 nm, the peak wavelength λ9≤m≤15 at the time that 9≤m≤15 is longer than or equal to 400 nm and shorter than or equal to 700 nm, and the peak wavelength λm≥16 at the time that m≥16 is shorter than or equal to 375 nm. Accordingly, this filter 100 is a multimode filter having seven peak wavelengths included in the target wavelength region W.
As noted above, a multimode filter can be achieved by appropriately designing the thickness of the intermediate layer 26 of a filter 100. Instead of the thickness of the intermediate layer 26, the refractive index of the intermediate layer 26 of the filter 100 may be appropriately designed. Alternatively, both the thickness and refractive index of the intermediate layer 26 of the filter 100 may be appropriately designed.
The following describes an example configuration in which the first reflective layer 28a and the second reflective layer 28b are each formed from a dielectric multi-layer film.
A dielectric multi-layer film includes a plurality of pair layers. One pair layer includes one low-refractive-index layer 27l and one high-refractive-index layer 27h. In the example shown in
In the example shown in
The following describes an example configuration of the filter array 10 for reducing restoration errors.
First, effects that are brought about in a case where a filter array 10 composed of a plurality of FP filters is used in a hyperspectral camera that performs restoration processing by compressed sensing are described.
In this formula, n and m represent the numbers of pixels in a longitudinal direction and a transverse direction, respectively. Ii,j represents the pixel value of the correct image in a pixel at a position (i, j). I′i,j represents the pixel value of an image in each wavelength band reconstructed in the pixel at the position (i, j).
In this example, the transmission characteristics of the filter array 10 are uniform across all bands; therefore, as shown in
Let it be assumed here that for light in an ith wavelength band (where i is an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, μi is the average of the transmittances of a plurality of optical filters included in the filter array 10. Let it be also assumed that the filter array 10 includes M (where M is an integer greater than or equal to 4) filters and Tij is the transmittance of a jth (where j is an integer greater than or equal to 1 and less than or equal to M) filter of the M filters for the light in the ith wavelength band. Then, the average μi of the transmittances is expressed by Formula (5) as follows:
Assuming that a is the standard deviation of the average μi of the transmittances for the N wavelength bands, σμ is expressed by Formula (6) as follows:
From the graph shown in
Let it be assumed here that for light in an ith wavelength band (where i is an integer greater than or equal to 1 and less than or equal to N) of the N wavelength bands, al is the standard deviation of the transmittances of a plurality of optical filters included in the filter array 10. σi is expressed by Formula (7) as follows:
The average μσ of the standard deviations σi of the transmittances for the N wavelength bands is expressed by Formula (8) as follows:
From the graph shown in
Instead of carrying out an evaluation with the average μσ of the standard deviations σi, an evaluation may be carried out with another index value that indicates contrast (i.e. a dynamic range) for each band of the filter array 10. For example, the index value Ri=(μi+3σi)/(μi−3σi), which takes the average transmittance into account, can be used.
The average μR of the index values Ri for all bands is expressed by Formula (9) as follows:
From the graph shown in
The optical nature of the filter array 10 in the foregoing discussions, i.e. the average transmittance and the standard deviation of the transmittances for each wavelength band, can be clarified by measuring and analyzing a histogram in any area including approximately six columns of pixels and approximately six rows of pixels. In a case where it is technically difficult to measure the transmission spectrum of such a filter array 10, it is possible to measure and analyze a histogram in a similar way by measuring a reflection spectrum for each wavelength band. Further, in a case where the filter array 10 is integrated on the image sensor 60, it is also possible to measure and analyze a histogram including the sensitivity characteristics of the image sensor 60 per se. Furthermore, in a case where each of the filters constituting the filter array 10 is an FP filter, there is in general a correlation between the thickness and histogram of a filter composed of a first reflective layer, a second reflective layer, and an intermediate layer disposed between the first reflective layer and the second reflective layer. For this reason, similar information can also be acquired by measuring a distribution of thicknesses in any area including approximately six columns of pixels and approximately six rows of pixels.
In a case where each of the filters constituting the filter array 10 is an FP filter, the transmittance tends to be higher in a wavelength band on a longer-wavelength side as described with reference to
A technology of the present disclosure is useful in a camera and a measuring instrument that acquire a multiwavelength image. The technology of the present disclosure is also applicable, for example, to biological, medical, and aesthetic sensing, food foreign material and residual pesticide testing systems, remote sensing systems, and on-board sensing systems.
Number | Date | Country | Kind |
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2020-005094 | Jan 2020 | JP | national |
Number | Date | Country | |
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Parent | PCT/JP2020/041439 | Nov 2020 | US |
Child | 17395927 | US |