A method for eliminating systematic errors in a partially coherent spatial light interference technique

Abstract

The present application relates to a kind of partial coherent spatial light interference technology system error elimination method, i.e. φ Popk With the difference between PC-SLIM experiment obtained φ Pop0 Between the difference between simulated calculation and PC-SLIM experiment obtained φ Gk , through repeated iteration, the system error of PC-SLIM technology can be eliminated, thereby greatly improving the accuracy of PC-SLIM technology, and then making it become a real optical precision detection technology. Since spatial light interference technology has axial sub-nanometer or even picometer optical path difference precision, if PC-SLIM system is changed to a reflective system, this method can also be applied to the surface precision detection of semiconductor chips.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical detection technology, and in particular to a system error elimination method of a partially coherent spatial light interference technology. BACKGROUND

[0002] Spatial light interference microscopy (SLIM) invented by Professor G. Popescu of the United States in 2011 has considerable influence as a typical quantitative phase imaging technology. The technology is based on a transmission-type Zernike phase contrast microscope and is suitable for observation of transparent samples such as biological cells, tissues and bacteria. However, the calculation model proposed by G. Popescu ignores the phase angle φ R (x) of the reference light, resulting in a system error in the calculation result of SLIM. In the measurement of red blood cells, the error can be more than 20%, and in the imaging of adherent cancer cells, the error can be more than 50%. This large system error makes SLIM technology not very practical and difficult to industrialize. My invention patent "A method for improving the precision of spatial light interference technology by double four-step phase shift method" (application number: 2022109236207) discloses a spatial light interference technology based on double four-step phase shift method, which can reduce the SLIM system error by more than half, greatly improving the precision of spatial light interference method. However, the use of double four-step phase shift method does not completely eliminate this system error, and the system error is still large in the imaging of adherent cancer cells. The main advantage of the double four-step phase shift method is that it can reduce the effective size of the phase contrast ring of the objective lens of the Olympus phase contrast microscope by about half. However, the reference light generated by the system is still the result of low-pass filtering of the object light wavefront, and the phase angle φ R (x) of the reference light is related to the ring thickness. As long as the ring thickness is not 0, the system error will always exist. This system error is reflected in the core calculation formula of SLIM technology:

[0003]

[0004] In addition, quantitative phase imaging technology has been developed since around 2000, but there is still no good product that can be generally accepted by the market. For example, the TIE technology based on the intensity propagation equation still has a relative error of 12%. The holographic tomographic microscopy (ODT) using laser, although the three-dimensional refractive index distribution of the sample can be measured by rotating the object or the illumination, but due to the laser speckle, the imaging signal-to-noise ratio is very low, and the Multilook technology used makes the imaging efficiency low. In contrast, the partially coherent spatial light interference technology has the advantages of high signal-to-noise ratio imaging of incoherent light, high stability of coaxial interference optical path and fast imaging of four-step phase shift method, so if the system error of SLIM can be completely eliminated, or the original default φR (x) is calculated by an algorithm, which is of great significance for the development of quantitative phase imaging technology and optical interference precision detection technology. SUMMARY

[0005] The present application aims to provide a system error elimination method of partial coherent spatial light interference technology, which is beneficial to eliminate the system error of PC-SLIM technology and improve the accuracy of quantitative phase imaging technology.

[0006] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a system error elimination method of partial coherent spatial light interference technology, comprising:

[0007] eliminate the phase result φ obtained by the partial coherent spatial light interference microscopy technology based on double four-step phase shift method, i.e. PC-SLIM technology, through the wavefront comparison iteration method based on PC-SLIM; Pop0 There is a system error between the real object light wavefront φ Real and the phase result φ obtained by the PC-SLIM technology; taking φ Pop0 as the input initial value, i.e. the initial guess value of the object light wavefront phase in the first operation φ G1 ; the initial guess value is the best initial value, which can make the subsequent calculation converge quickly;

[0008] The wavefront comparison iteration method based on PC-SLIM calculates the PC-SLIM imaging process by computer, and performs high-pass filtering and low-pass filtering on the object light wavefront in the kth iteration to obtain the scattered light and direct light respectively:

[0009]

[0010] Wherein, u Sk (x) represents the scattered light, u Dk (x) represents the direct light or reference light, h HS (x) represents the transfer function of high-pass filtering, h LS (x) represents the transfer function of low-pass filtering, k represents the kth iteration calculation, F[] represents the Fourier transform, x is the spatial coordinate vector, and φ Gk is the kth guess of the object light wavefront;

[0011] Then, according to the imaging model of PC-SLIM technology, we have:

[0012] φ SLIMk (x) = angle[u Sk (x)] - angle[u Dk (x)] = φ Sk (x) - φ Rk (x)

[0013] ​

[0014] where φ SLIMk (x) represents the phase angle of the scattered light minus the angle of the direct light or reference light; angle[] represents the angle operation of the complex wavefront, φ Sk (x) represents the phase angle of the scattered light, φ Rk (x) represents the phase angle of the direct light or reference light, |u Real (x)| represents the amplitude of the real object wavefront, φ Popk represents the phase angle obtained by the imaging model of the PC-SLIM technology in the kth iteration;

[0015] This φ Popk is compared with the initial φ Pop0 , and the difference between the two is obtained:

[0016] Δφ k = φ Pop0 - φ Popk

[0017] If the difference between φ Popk and the initial φ Pop0 is less than the change in the difference in the previous iteration by a set threshold ε:

[0018]

[0019] or the difference between φ Popk and the initial φ Pop0 is less than the set threshold ε:

[0020]

[0021] φ Gk is taken as the result output and the iteration is exited; the obtained φ Gk is the object wavefront φ Real (x) after the system error is eliminated.

[0022] If neither condition is met, φ Gk is updated as:

[0023] φ Gk+1 = φ Gk + Δφ k

[0024] Then the iteration continues.

[0025] Further, the equivalent aperture stop of the high-pass filter and the low-pass filter of the PC-SLIM system is respectively represented as:

[0026]

[0027]

[0028] where H L is the geometry of the objective's phase contrast ring, H H is the geometry of the objective's back pupil minus H L is the geometry of the back remaining part, H S is the geometry of the system's illumination source, v is the spatial frequency vector, v0 is the spatial frequency vector corresponding to the offset coordinate where the maximum overlap area occurs, and φ S is the phase of the wavefront at the plane of the spatial light modulator H H is the phase of the wavefront at the plane of the spatial light modulator H

[0029] Compared with the prior art, the present application has the following beneficial effects: a system error elimination method of a partial coherent spatial light interference technology is provided, the method is a wavefront comparison iteration method based on PC-SLIM technology, the difference between φ Popk and φ Pop0 obtained by PC-SLIM is compared, the guessed value φ Gk of the original wavefront is quickly updated and iterated, the system error of PC-SLIM technology is eliminated through repeated quick iteration, and therefore the accuracy of quantitative phase imaging is greatly improved, and the PC-SLIM technology becomes a real optical precision detection technology. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is the system optical path diagram of PC-SLIM in the embodiment of the present application.

[0031] Figure 2 is the method implementation flowchart of the embodiment of the present application.

[0032] Figure 3 is the three-dimensional phase diagram of red blood cells obtained by PC-SLIM reconstruction in the first embodiment of the present application.

[0033] Figure 4is the three-dimensional phase image of red blood cells obtained by the wavefront iteration method in the embodiment one of the present application.

[0034] Figure 5 is the profile of the phase image of red blood cells in the embodiment one of the present application.

[0035] Figure 6 is the three-dimensional phase image of red blood cells obtained by the PC-SLIM reconstruction in the embodiment two of the present application.

[0036] Figure 7 is the three-dimensional phase image of red blood cells obtained by the wavefront iteration method in the embodiment two of the present application.

[0037] Figure 8 is the profile of the phase image of red blood cells in the embodiment two of the present application. DETAILED DESCRIPTION

[0038] The present application is further described below in conjunction with the accompanying drawings and embodiments.

[0039] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0040] It is to be understood that the singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. It is to be understood that the terms "comprising," "including," and "having" can be used interchangeably.

[0041] The system error elimination method of the partial coherent spatial light interference technology provided by the embodiment is based on the hardware configuration of the Olympus phase contrast microscope, based on the partial coherent spatial light interference microscopy technology, and uses a double four-step phase shift method to reduce system errors and obtain a better calculation initial condition. The main imaging objects of the embodiment can be blood cells, adherent cells which are not too thick, and other transparent samples. The amplitudes of these samples are substantially constant, i.e., independent of space, and the phase change is not very dramatic, satisfying the Rytov approximation condition, i.e., the phase is slowly varying. Figure 1 The system optical path diagram of the PC-SLIM in the embodiment is shown.

[0042] As Figure 2As shown, the system error elimination method of the partial coherent spatial light interference technology provided in the embodiment is a wavefront comparison iteration method based on PC-SLIM, and the experimental result φ Pop0 is obtained by the partial coherent spatial light interference microscopy technology (PC-SLIM technology) based on the double four-step phase shift method G1 . The PC-SLIM based on the double four-step phase shift method obtains the measurement result conforming to the partial coherent light phase contrast imaging theoretical model on the basis of the hardware configuration of the commercial phase contrast microscope, which ensures the fast convergence characteristics of the algorithm.

[0043] The object wavefront φ is obtained by computer simulation of the PC-SLIM imaging process, and the object wavefront φ

[0044]

[0045] wherein u Sk (x) represents the scattered light, u Dk (x) represents the direct light or reference light, h HS (x) represents the transfer function of the high-pass filter, h LS (x) represents the transfer function of the low-pass filter, k represents the kth iteration calculation, F[] represents the Fourier transform, x is a spatial coordinate vector, and φ Gk is the kth guess of the object wavefront. The equivalent aperture diaphragms of the high-pass filter and the low-pass filter of the PC-SLIM system are respectively represented as:

[0046]

[0047] wherein the aperture diaphragm H L is the geometric shape of the phase contrast ring of the objective lens, the aperture diaphragm H H is the geometric shape of the back pupil of the objective lens excluding the remaining part of H L , and H S is the geometric shape of the system illumination light source, v is a spatial frequency vector, and v0 is the spatial frequency vector corresponding to the offset coordinates at which the aperture diaphragms H S and H H are spatially offset and have the maximum overlapping area, at which time the three-dimensional cross-correlation transfer function (TCC function) of the system takes the maximum value.

[0048] Then, according to the imaging model of the PC-SLIM technology, there is:

[0049]

[0050] The phase of the object wavefront is updated. Wherein φ SLIMk(x) represents the phase angle of the scattered light, φ Sk (x) represents the phase angle of the scattered light, φ Rk (x) represents the phase angle of the reference light, |u Real (x) represents the phase angle of the reference light, |u Popk represents the phase angle of the PC-SLIM imaging model of the kth iteration.

[0051] This φ Popk is compared with the initial φ Pop0 , and the difference between them is obtained:

[0052] Δφ k = φ Pop0 - φ Popk (4)

[0053] If the difference is not changed much compared with the difference in the last iteration, in this embodiment, the change is less than 2%, then φ Gk can be output as the result and the iteration is exited.

[0054]

[0055] If the difference between φ Popk and the initial φ Pop0 is already very small, in this embodiment, the difference is less than 2%, then φ Gk can be output as the result and the iteration is exited.

[0056]

[0057] If neither of the two conditions (5) and (6) is satisfied, the iteration is continued, and φ Gk is updated as:

[0058] φ Gk+1 = φ Gk + Δφ k (7)

[0059] Then the calculation after (1) is repeated.

[0060] Finally, because of the repeated use of Fourier transform in the iteration, the wavefront comparison iteration method converges rapidly, and has the characteristics of the fast convergence of the GS algorithm, and only a few iteration times (such as 3 times) are needed to converge well.

[0061] Figure 3 The red blood cell image obtained by the PC-SLIM reconstruction in Example 1 is shown. Figure 4The three-dimensional phase profile of the original red blood cell is shown in the embodiment one, which is obtained by the wavefront iteration method. Figure 5 The profile of the red blood cell phase image is shown in the embodiment one, which is Figure 4 The profile of the red blood cell at the center line converges to the original red blood cell wavefront in three iterations of the wavefront iteration method. The wavefront iteration method converges quickly, and the total number of iterations is three. The straight line marked with a cross represents the phase angle φ of the scattered light of the high pass S The unmarked solid line represents the angle φ obtained by the PC-SLIM experiment Pop0 The straight line marked with a plus represents the φ obtained by the wavefront iteration method at the kth iteration Popk As shown in Figure 5 After three iterations of the method, the straight line marked with a plus quickly approaches the unmarked solid line. The straight line marked with o is the guess value φ given by the algorithm of the wavefront iteration method at the kth iteration Gk When the straight line marked with a plus coincides with the unmarked solid line, the φ Gk is the required original true wavefront of the red blood cell.

[0062] Figure 6 The red blood cell image obtained by the PC-SLIM reconstruction is shown in the embodiment two. The number of red blood cells is small, and the resolution is high. Figure 7 The three-dimensional phase profile of the original red blood cell is shown in the embodiment one, which is obtained by the wavefront iteration method. Figure 8 The profile of the red blood cell phase image is shown in the embodiment two, which is Figure 7 The profile of the red blood cell at the center line converges to the original red blood cell true wavefront in three iterations of the wavefront iteration method. The fast convergence process of the wavefront iteration method can be more clearly seen, and the total number of iterations is three.

[0063] The above two examples both use the partial coherence spatial light interference technology based on the double four-step phase shift method, obtain the measurement results consistent with the partial coherence light phase contrast imaging theoretical model on a commercial phase contrast microscope (Olympus phase contrast microscope IX73), and then carry out simulation and calculation.

[0064] The above is only the preferred embodiment of the present application, and is not intended to limit the other forms of the present application. Any skilled person in the art can modify or change the above disclosed technical content to equivalent embodiments. However, any simple modification, equivalent change and modification made according to the technical essence of the present application to the above embodiments, without departing from the technical solution content of the present application, still falls within the protection scope of the present application.

Claims

1. A method for system error elimination in a partially coherent spatial optical interferometry technique, characterized in that, Comprising: Eliminate the systematic error between the real object wave front φ Pop0 and the phase result φ Real obtained by the partial coherent spatial light interference microscopy based on double four-step phase shift method (PC-SLIM) through the wave front comparison iterative method based on PC-SLIM Pop0 ; take φ G1 as the initial guess value of the object wave front phase in the first operation, which is the best initial value and can make the subsequent calculation converge quickly The PC-SLIM based wavefront comparison iterative method calculates the object light wavefront of the kth iteration by computer simulation of the PC-SLIM imaging process High-pass filtering and low-pass filtering are performed to obtain scattered light and direct light respectively as: where u Sk (x) denotes the scattered light, u Dk (x) denotes the direct light or reference light, h HS (x) denotes the high-pass filtered transfer function, h LS (x) denotes the low-pass filtered transfer function, k denotes the kth iteration calculation, F[] denotes the Fourier transform, x is a spatial coordinate vector, φ Gk is the kth guess of the object light wave front; Then by the imaging model of PC-SLIM technique, we have: φ SLIMk (x) = angle[u Sk (x)] - angle[u Dk (x)] = φ Sk (x) - φ Rk (x) where φ SLIMk (x) denotes the phase angle of the scattered light minus the angle of the direct light or reference light; angle[] denotes the angle operation of the complex wavefront, φ Sk (x) denotes the phase angle of the scattered light, φ Rk (x) denotes the phase angle of the direct light or reference light, |u Real (x) | denotes the amplitude of the real object wavefront, φ Popk denotes the phase angle obtained by the imaging model of the kth iteration of the PC-SLIM technique; Take this φ Popk and compare it to the original φ Pop0 and take the difference between the two. Δφ k = φ Pop0 - φ Popk If φ Popk With the initial φ Pop0 The change in the difference compared to the difference in the previous iteration is less than the set threshold ε: or φ Popk the difference between the initial φ Pop0 is less than a set threshold ε: then φ Gk as a result output and exit the iteration; the resulting φ Gk is the object wavefront φ Real (x); If neither condition is met, then update φ Gk is: φ Gk+1 = φ Gk + Δφ k Then the iteration is continued.

2. A method for eliminating systematic errors in a partially coherent spatial optical interferometry system according to claim 1, characterized in that, The equivalent aperture stop of the high-pass filter and the low-pass filter of the PC-SLIM system are denoted as: where H L is the geometry of the phase contrast ring of the objective, H H is the back pupil of the objective minus H L is the geometry of the remaining back portion, H S is the geometry of the system illumination source, v is the spatial frequency vector, and v0 is the spatial frequency vector of the aperture H S is the spatial frequency vector of the aperture H H is the spatial frequency vector of the aperture H

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