Patent Application
20190101380
The invention is from the field of optics. Specifically the invention is from the field of phase shift interferometry.
Phase shift interferometry (PSI) is a well-established optical technique enabling high resolution non-contact and fast measurement of the distance between an object and some arbitrary plane perpendicular to the optical axis of the system. Based on this capability, PSI enables both tracking and analyzing the time dependent relative position of an object at a single point along the optical axis using a single pixel detector, and the three dimensional (3D) topographical mapping of an object's surface either in a single shot using an array of detectors or by scanning its surface using a single pixel detector. Such capabilities are of great importance and have applications in many scientific fields and in industry requiring fast high resolution surface mapping or motion tracking/vibrometry, such as the semiconductor industry, micro-electronics industry, biomedical imaging etc.
In PSI the relative position of the measured points on the surface of the object is extracted from the phase of the interference signal, which is extracted from several (i.e. 3-4) phase shifted interference signals obtained by measurements that are performed sequentially or in parallel. Since the phase can only be determined up to multiples of 2π, the change in an object's relative position or changes in its topography can be determined with a certainty only for differences in position that induce less than 2π change in the phase. In an optical system relying on a single wavelength λ and reflection measurement geometry, this 2π phase change translates to differences in position that are up to only λ/2 which is relatively short for optical wavelengths. This limitation cripples the ability to measure topographies with large height variability and high speed motions. One of the approaches to resolve this problem is using phase unwrapping algorithms; however they are limited in their accuracy. However, this limitation can be overcome by performing the interferometric measurements using several wavelengths (multiple wavelength PSI), either in parallel or sequentially, and combining them to yield an effective wavelength also known as a beat wavelength which is much longer than each of the wavelengths used and can thus lead to better performance even up to several orders of magnitude. This process and technique have been presented and discussed in U.S. patent application Ser. No. 15/260,398 entitled “Multiple Wavelengths Real Time Phase Shift Interference Microscopy” to the inventors of the present invention.
PSI systems using several wavelengths for topography or movement measurements are complicated optical systems that require several detectors and complementary optical equipment in order to measure sequentially or in parallel the phase shifted interferometric signals for each of the wavelengths in order to extract the required phase information. In the sequential measurement, the interferometric signals should be measured for the different phase shifts and then for each wavelength—this can be time consuming and can considerably harm the accuracy of the measurement as the object moves between measurements in addition to the obvious implication on the measurement rate. In the parallel detection approach, the different phase shifted interferometric signals should be measured simultaneously for the different wavelengths and for the different phases for each of them, requiring a large number of detectors and optics for the separation or extraction of the different wavelengths.
It is therefore a purpose of the present invention to provide PSI systems using several wavelengths that are configured to be used with a simplified method for performing the multiple wavelength measurement.
Further purposes and advantages of this invention will appear as the description proceeds.
In a first aspect the invention is a method for performing multiple wavelength phase shift interferometry (PSI). The method comprises:
In embodiments of the method at least two of the N wavelengths originate from the same light source and their beat modulation frequencies are chosen to be much higher than the detector cutoff frequency.
In embodiments of the method the process of frequency domain demodulation comprises one of:
In an embodiment of the method:
In an embodiment of the method:
In an embodiment of the method:
a) in step “d” the interferometer is an orthogonally polarized phase shift interferometer;
b) in step “e” the combined light beam output signal of the interferometer is detected by a segmented detector comprised of M segments, wherein a polarizer and a phase retardation mask, each shifting the phase by a different amount, are located in front of each segment of the detector;
In a second aspect the invention is a system for performing multiple wavelength phase shift interferometry (PSI). The system comprises:
a) at least one light source, wherein all light sources together provide N beams of monochromatic light at N distinct wavelengths, wherein N≥2;
In embodiments of the system the frequency domain demodulation unit comprises one of:
In embodiments of the system the frequency domain demodulation unit and the processor and display unit are implemented as a single combined unit that shares processing, memory, and display components.
In embodiments of the system at least two of the N wavelengths originate from the same light source and their beat modulation frequencies are chosen to be much higher than the detector cutoff frequency.
In an embodiment of the system:
In an embodiment of the system:
In an embodiment of the system:
In this embodiment a polarization mask, which comprises polarization axes each of which is oriented at a different angle, can be located in front of each segment of the segmented detector in place of the polarizer and the phase retardation mask. The polarization mask comprises polarization axes having at least three orientations in each segment. For example the at least three orientations can be either 0, 45 and 90 degrees; or −45, 0 and 45 degrees; or 30, 60 and 120 degrees; or other combinations.
In another variation of this embodiment the segmented detector is a parallel detector or camera with a polarization mask in front of its photo sensing pixels. The polarization mask is divided into regions of 4 pixels, wherein the polarization mask comprises a polarizer having a different orientation for each of the 4 pixels. The orientations can be, for example, 0, 45, −45, and 90 degrees or other combinations.
All the above and other characteristics and advantages of the invention will be further understood through the following illustrative and non-limitative description of embodiments thereof, with reference to the appended drawings.
Herein is provided a simplified method for performing multiple wavelength PSI measurements that is implemented by modulating each of the monochromatic light sources with a different carrier frequency, combining them to a single beam, detecting them all using the same detectors and separating them via Fourier analysis and demodulation of the data—thus performing the detection of all wavelengths simultaneously and by using the same detectors. This approach offers both a simplification to the optical system and reduces the duration of time required to perform the multiple wavelength measurement, based on a simple data extraction algorithm decoding the information for each wavelength.
In PSI, a two beam interferometer is normally used to produce the interference pattern of a sample positioned in one of the interferometer arms. In such an interferometric system a continuous monochromatic source with relatively constant amplitude is used. The reflected interference signal's intensity from each point of the sample can be described by a biased harmonic behavior described in equation 1:
I=B+A cos ϕ (1)
Wherein, B is the bias or DC level, A is the envelope of the interferometric signal and φ is its phase. The interference phase is related to the optical path difference (OPD) between a given point on the sample and its respective point of the reference mirror placed in the second arm of the interferometer, and it encodes the relative distance of the point relative to a plane with equal distance to the length of the interferometer arm holding the mirror. In order to extract the phase from the interferometric signal, using several (here 3) phase shifted signals, as can be seen in equations 2 and 3, where i=1,2,3 stands for the three phase shifted signals.
I
i
=B+A cos(ϕ+(i−1)π/2) (2)
ϕ=tan−1[(I1+I3−2I2)/(I1−I3)] (3)
However, such measurements are limited in their ability to unambiguously determine the OPD and therefore the distance between the sample point and the reference mirror plane, as the intensity signal is a harmonic signal with a phase of φ which is related to the OPD as described in equation 4, and is therefore limited to phase differences of 2π, which translates in reflection geometry to OPD of λ/2.
When the sample has height variations larger than λ/2, the distance or 3D topography of the sample cannot be determined without ambiguity since the extracted phase values are wrapped by 2π modulus. In order to reconstruct the 3D shape of the sample's surface i.e. the distance between two adjacent points on its surface or the distance that the same point has moved along the optical axis of the system between measurements, either a phase unwrapping algorithm must be implemented or a utilization of 2 (or more) wavelengths for measurement. For multiple wavelengths, the interference signal's intensity of equation 2 is measured for all wavelengths separately and for each of the phase shifts, and using a combination of the phases calculated for each, one can extract the OPD for higher height variations using the technique presented in the previously referenced U.S. Ser. No. 15/260,398.
In order to achieve this extraction, for example for 3 wavelengths, an overall of 9 interferometric signals have to be taken for a single interferometric measurement of the sample—3 for each phase shifted interferometric signal and 3 for each wavelength. This can be achieved by taking them sequentially, in parallel or in some hybrid of these—each option requiring a different number of detectors or with varying measurement duration until the acquisition of the data required for a single shot of interferometric measurement is completed. This process is to be repeated if the sample changes its surface shape, or if it is in motion and its movement is being analyzed by the system such as in vibrometry.
Since either a large number of sequential measurements or a large number of detectors is required for a single interferometric measurement, the inventors have found a method of minimizing the number of required detectors, simplifying the optical setup and possibly shortening the measurement time to a single shot. This is achieved by combining the concept of parallel phase shift interferometry enabling the measurement of the 3 phase shifted signals in parallel by 3 separate detectors simultaneously, and performing the measurement of the different wavelengths simultaneously on the same detectors instead of multiplying the number of detectors by 3 or taking the measurements sequentially.
A single shot measurement can be achieved by using physical band pass filters to separate the carrier frequencies (and thus wavelengths). In the case of frequency separation by Fourier analysis it might be necessary to buffer several measurements to extract the Fourier signal using a sequence of measurements used for a discrete Fourier transform (DFT). Alternatively a sliding window FT can be performed, in which case it is necessary only to buffer samples at the beginning of the measurement and then output a position measurement at each sampling time of an analog-to-digital converter.
In all cases measurement time shortening is achieved by the fact that no change in the system is performed, such as a change of source wavelength or phase retardation such as in sequential measurements.
I
s,λ
(t)=/Iλ
The sources are then combined by beam combining optics 12 into a single beam that functions as the light source for two beam phase shift interferometer 28. The combined beam travels to beam splitter 14 in interferometer 28 wherein part of the beam passes to a sample 16 mounted on a moveable stage. The other part of the combined beam passes through phase modulating optics 20 to a mirror 18, which can be either fixed or mounted on a stage with controlled motion. The beams reflected from sample 16 and mirror 18 are recombined by beam splitter 14 and the three modulated wavelength signals are then measured in parallel using a single detector 22 while the different required phase shifts are performed sequentially by changing the phase shift introduced by the phase modulating optics 20. The intensity of each of the phase shifted signals for each wavelength is extracted in frequency demodulation unit 24 by a process of frequency domain demodulation known in the art such as by Fourier transform or using electronic bandpass filters and the three demodulated signals are sent for further processing and display to processor and display unit 26.
In embodiments of the system shown in
In this embodiment light at wavelengths λ(1), λ(2), and λ(3) emitted by three monochromatic light sources 10(1), 10(2), and 10(3) are each modulated respectively by three well separated and different frequencies f(1), f(2) and f(3). The output intensity of each light source has the form shown in equation 5. The sources are then combined by beam combining optics 12 into a single beam that functions as the light source for two beam orthogonal polarization interferometer 28. The combined beam travels through optical elements 30 to interferometer 28′. For example, optical elements 30 can comprise one or more of the following components: a polarizer, a polarized beam splitter and an achromatic quarter wave plates; grating based polarized splitting elements; a Wollaston prism; a Rochon polarizer; polarization conversion mirrors; and a combination of achromatic waveplates and liquid crystal devices. In addition to introducing optical elements 30, the beam splitter 14 in interferometer 28 (see
A common path orthogonal polarization interferometer is another embodiment of an optical system for which the method of the invention can be used. For example when a polarized beam passes through or is reflected from a birefringent element, it splits into two orthogonally polarized beams which nearly traverse the same path and may be considered as common path interferometers when the beams are recombined. When the beam is incident at normal incidence the two orthogonally polarized components traverse exactly the same path, yet their phases are different. In nematic liquid crystal devices the extraordinary phase can be modified using an applied voltage while the ordinary one which can be considered as a reference beam is not changed. Another configuration is when a polarized beam is obliquely incident on isotropic medium composed of a single interface or multiple interfaces. In this case the reflected or transmitted TE and TM waves accumulate different phases but traverse the same path; hence after recombining the two beams using a polarizing element, this configuration acts like a common path orthogonal polarization interferometer. This last configuration is used in ellipsometry as a methodology to measure the refractive indices and thicknesses of layers.
Herein embodiments of the invention are described using three different wavelengths with the different wavelengths coming from three different sources and therefore they do not interfere. However in general the invention can be carried out using at least two different wavelengths. Alternatively two of the wavelengths or more can originate from the same light source but their beat modulation frequency will be chosen to be much higher than the detector cutoff frequency so that no extra time modulation is observed by the detector except for the modulation frequencies fk. In these cases the intensity pattern on each detector for each of the phase shifts denoted by I, is a sum of the three interferometric signals resulting from the interferometric signals (denoted by k) of the three wavelengths as is given in equation 6, which result from a combination of equations 2 and 5.
By taking the Fourier transform of equation 6 a frequency domain signal is received that is composed of the three delta function pairs around frequencies f(1), f(2) and f(3) each having an amplitude which is the Fourier transform of the corresponding term in the squared brackets in equation 6 as is given in equation 7.
By filtering each of the frequencies fk using a band-pass filter around each of the frequencies, the amplitude can be measured and the interferometric signal extracted for each of the wavelengths λk.
This in turn allows the phase for each wavelength to be extracted as it is done in the regular PSI, and combining them to extract the unwrapped phase allowing measuring larger height differences and longer movements based on the inventor's multiple wavelengths PSI technique. The frequency demodulation can be done algorithmically using Fourier transform or electronically using band-pass filtering hardware.
In another embodiment a parallel or segmented detector can be used with achromatic phase retardation mask and polarizer in front of its segments so that each segment receives interference signal that has undergone one specific phase retardation shift. A camera can be used with periodic phase retardation mask and polarizer to obtain phase shift imaging with phase unwrapping using multiple wavelengths. The phase mask can be made of achromatic liquid crystal waveplates for example or subwavelength gratings with different thicknesses, refractive indices or grating periods so that they produce different form birefringence which in turn produces the phase retardation shifts.
In the system shown in
In another variation of the system shown in
In embodiments of the systems shown in
The systems shown in
Using the system of
The method of the invention and the embodiments of systems described above can advantageously be employed to:
Although embodiments of the invention have been described by way of illustration, it will be understood that the invention may be carried out with many variations, modifications, and adaptations, without exceeding the scope of the claims.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/IL2017/050335 | 3/16/2017 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62311438 | Mar 2016 | US |
