A method for improving the accuracy of spatial optical interferometry using a double four-step phase shift method

Abstract

The present invention relates to a method for improving the precision of spatial light interferometry using a double four-step phase shift method. The method utilizes the Zernike phase contrast microscope imaging model derived from the theory of partially coherent light. The PC-SLIM model, a computational model derived from spatial light interferometry research based on the theory of partially coherent light, is used as the computational model. The method performs two four-step phase shifts to form eight images. The first four-step phase shift uses an existing four-step phase shift method to measure the object phase. The second four-step phase shift uses a mosaic grating or a spectroscopic grating superimposed on the SLM to alter the system's cross transfer function (TCC) to measure the object phase. This method is beneficial for improving the precision of spatial light interferometry.

Description

Technical Field

[0001] The present invention belongs to the field of optical detection, and in particular relates to a method for improving the precision of spatial light interference technology by using a double four-step phase shift method. Background Art

[0002] Spatial light interference microscopy, invented by American Professor G. Popescu in 2011, has become a highly influential quantitative phase imaging technique. Based on Zernike phase contrast microscopy, it is suitable for observing transparent samples such as biological cells, tissues, and bacteria. Figure 1 It is the optical path of spatial optical interferometry technology. Figure 2 The grating used in the four-step phase shift method. Before the 1990s, engineers and scientists focused their research on Zernike phase contrast microscopes on optimizing phase contrast ratios. Phase plate size, phase shift, and transmittance were all highly optimized. Its design premise was for imaging objects with weak phase (phase far less than 1 rad). Zernike phase contrast microscopes were later categorized as qualitative measurement methods. The Olympus IX73 phase contrast microscope is a representative example. Professor G. Popescu further creatively used the four-step phase shift method to reconstruct the three-dimensional phase profile of transparent objects, transforming Zernike phase contrast into spatial interferometry—a quantitative phase imaging technique. Spatial interferometry has been well-received due to its higher signal-to-noise ratio and high imaging efficiency compared to quantitative phase imaging techniques using laser illumination. However, research has revealed that the technique is still relatively crude and exhibits several significant challenges. For example, the technique advocates the use of white light, but the white light spectrum of halogen lamps deviates significantly from a Gaussian spectrum. The advantage of a Gaussian spectrum is that its Fourier transform remains Gaussian. A non-Gaussian white light spectrum will cause the calculation results of the four-step phase shift method to deviate from the Gaussian model, resulting in errors. Therefore, some researchers use a green light filter with a central wavelength of 546 nm in the optical path to achieve Gaussian illumination. The only benefit of using a wider bandwidth of white light is that its coherence length is shortened, facilitating the use of a coherence gate to exclude out-of-plane light signals, thus facilitating the extension of SLIM to SLIT, a spatial optical interferometry tomography technique invented by G. Popescu.

[0003] The key point is that some scholars, based on the theory of partial coherence, have discovered that there is still a major problem in the measurement accuracy and theoretical calculation of G. Popescu's spatial light interferometry technology. Traditional patents and papers on spatial light interferometry technology often mistakenly believe that the accuracy provided by the four-step phase shifting method, an optical interferometry technique itself, is the accuracy of spatial light interferometry technology. In fact, this accuracy is the accuracy of the four-step phase shifting method as an optical interferometry technique itself. The systematic error of spatial light interferometry technology actually comes mainly from the angle of direct light (or reference light) that is not a plane wave. Zernike phase contrast microscopes using epi-illumination methods cannot perform pinhole filtering like laser illumination, so spatial light interferometry technology is far from being able to compress the angle of the reference light to 0.

[0004] The calculation model of G. Popescu's spatial optical interferometry technology paper or patent is relatively simple, mainly including the following formula:

[0005]

[0006]

[0007] φ SLIM =angle((I0-I2)+j(I3-I1))

[0008] φ o (x)=φ Pop (x)+φ R (x),φ SLIM (x)=φ H (x)-φ R (x)

[0009] At the same time, the relationship between object light, scattered light and direct light can be expressed by complex vectors as follows: Figure 3 .Depend on Figure 3 It can be seen that the angle of the reference light or direct light is defaulted to 0, which is the root of the problem.

[0010] Taking the polystyrene microspheres immersed in oil with a 6-micron objective lens as an example, the maximum phase height is 274.5°. Based on the theory of partially coherent light, the spatial light interference of the oil-immersed microspheres using the 20x phase contrast objective lens of the Olympus phase contrast microscope IX73 can be simulated to obtain Figure 4 Simulation results. The Highpass curve in the figure represents the angle of scattered light of the system high-pass or band-pass filtering, i.e. φ H The scattered light passes through the portion of the lens outside the pupil phase plate. The Ref curve is the angle of direct light. Direct light passes through the pupil phase plate. Figure 4 It can be seen that the reference light angle of the microsphere has a distribution, the center of which is about -29°. The highest points of each curve in the figure are:

[0011] φ Real=274.5°,φ SLIM =293.5°,φ Pop =310°,φ R =29°

[0012] The angle φ obtained according to Popescu's theoretical model Pop Ratio φ Real It is 36° higher (the theoretical value should be 29°, but the phase loop simulation edge sampling error leads to the simulation result of 36°). Without further optimization of the system, the phase measurement accuracy of the four-step phase shift method is calculated according to the formula σ φ =σ n / 4U S U D It easily reaches 0.5°, corresponding to an optical path difference accuracy of 0.76nm. This means that the error in Popescu's calculation is far greater than the 0.5° accuracy of the four-step phase shift method. This shows that under the standard configuration of Olympus phase contrast microscopes, the angle of the reference beam causes the accuracy or precision of the actual measurement results of spatial interferometry to be far inferior to that of the four-step phase shift method, and becomes the main source of systematic error in spatial interferometry.

[0013] Furthermore, quantitative phase imaging technology, which began development around 2000, still lacks a proven product that has achieved widespread market acceptance. For example, TIE technology still suffers from a 20% relative error. While laser-based quantitative phase imaging can measure the three-dimensional refractive index of a sample by rotating the object or illuminating it, laser speckle results in a very low signal-to-noise ratio, making imaging speed inefficient. In contrast, spatial interferometry using partially coherent illumination offers high signal-to-noise ratio imaging and the rapid imaging speed of the four-step phase shifting method. Therefore, further improving the accuracy or precision of Popescu's spatial interferometry technology is of great practical significance. Summary of the Invention

[0014] The purpose of the present invention is to provide a method for improving the precision of spatial light interferometry technology by using a double four-step phase shift method, which is beneficial to improving the precision of spatial light interferometry.

[0015] To achieve the above objectives, the technical solution adopted by the present invention is: a method for improving the accuracy of spatial light interferometry technology using a double four-step phase shift method, and using the partially coherent light theory to obtain the Zernike phase contrast microscope imaging model:

[0016]

[0017] Among them, I i (x) is the intensity of the i-th phase contrast imaging; x is the spatial coordinate; I D (x) is the intensity of direct light or reference light; I S(x) is the intensity of scattered light; F(μ) is the spatial frequency distribution of object light; H S (ξ) is the aperture of the light source, H L (μ) is the aperture of the phase ring; H H (μ) is the removal of H L (μ) is the outer aperture; t is the transmittance of the phase plate; Δφ is the modulation angle of the four-step phase shift method; Re is the real part operation.

[0018] Furthermore, the calculation model adopts the PC-SLIM model, which is a calculation model obtained by studying spatial light interference technology based on the theory of partially coherent light, and mainly includes the following formulas:

[0019]

[0020] a(x)=(I1+I3) / 2+Δn=(I0+I2) / 2+Δn

[0021]

[0022] φ SLIM (x) = angle ((I0-I2) + j (I3-I1))

[0023] φ o (x)=φ SLIM (x)+φ R (x),φ Pop (x)=φ H (x)-φ R (x)

[0024]

[0025] Among them, I n (x) is the intensity of the phase contrast image obtained by the four-step phase shift method, a(x) = I S (x)+I D (x); Δ(x) is a modulated intensity term obtained by approximating the cross transfer function (TCC) of the Zernike phase contrast microscope; Δn is the noise of the CMOS or CCD; f(x) is the complex transmittance of the object; where φ SLIM is the angle measurement result of the four-step phase shift method; h S (x) = F -1 (H S (μ));h H (x) = F -1 (H H (μ));h L (x) = F -1 (H L (μ)); φ ois the phase angle of the complex wave front of the object; φ R is the wavefront angle of the reference light; φ Pop is the phase angle reconstructed by SLIM technology, φ H is the wavefront angle of scattered light; U o =|u o |;

[0026] Furthermore, the four-step phase shift method is performed twice, resulting in eight images. The first four-step phase shift method uses the existing four-step phase shift method to measure the object phase. The second four-step phase shift method uses a mosaic grating or a blazed grating superimposed on the SLM to change the cross transfer function (TCC) of the system to measure the object phase. The angle of the scattered light remains unchanged in the two measurements, but the reference light angle of the second four-step phase shift method is much smaller than that of the first. The phase is calculated using the following formula:

[0027] Δφ R =Δφ SLIM =φ SLIM1 -φ SLIM2

[0028] φ D4 =φ Pop1 -Δφ R

[0029] Among them, φ SLIM1 is the measurement result of the first four-step phase shift method, φ SLIM2 is the measurement result of the second four-step phase shift method, Δφ R is the reference light angle change between the two measurements, φ D4 This is the final calculation result of the SLIM technology using the double four-step phase shift method.

[0030] Compared with the prior art, the present invention has the following beneficial effects: the present invention provides a method for improving the accuracy of spatial light interferometry technology by using a double four-step phase shift method, which can reduce the system error by more than half and greatly improve the accuracy of spatial light interferometry. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is the optical path of traditional spatial light interference microscopy technology.

[0032] Figure 2 These are four gratings of the traditional four-step phase shift method.

[0033] Figure 3 The object light vector is obtained by adding the direct light vector to the scattered light vector.

[0034] Figure 4 This is the simulation result of spatial light interference of 6-micron oil-immersed microspheres.

[0035] Figure 5 These are correlation diagrams of the TCC function used in an embodiment of the present invention. (a) The leaf-shaped TCC function of an Olympus phase contrast microscope, when the object function is one-dimensional; (b) The approximate TCC function after variable separation; (c) The horizontal and vertical cross-sections at the highest point in figure a; and (d) The difference between functions a and b. (Each pixel is 4.5 microns.)

[0036] Figure 6 It is a blazed grating used in an embodiment of the present invention for directly removing the inner and outer edge portions of the ring.

[0037] Figure 7 It is a mosaic grating used in an embodiment of the present invention to make the contribution of the inner and outer edge portions of the ring to the TCC integral result of the interference term equal to 0.

[0038] Figure 8 The following are a bright field image of an 8.4-micron microsphere and a 3D image of the microsphere phase reconstruction, respectively. (a) Bright field image of an 8.4-micron microsphere; (b) 3D image of the microsphere phase reconstruction.

[0039] Figure 9 This is the result of spatial light interference reconstruction of oil-immersed microspheres using the double four-step phase shift method in an embodiment of the present invention.

[0040] Figure 10 This is the simulation result of traditional spatial light interference of 8.4-micron microspheres in an embodiment of the present invention.

[0041] Figure 11 It is used in the embodiment of the present invention Figure 6 or 7 gratings for 8.4 μm microspheres.

[0042] Figure 12 This is a flowchart of a method implementation in an embodiment of the present invention. DETAILED DESCRIPTION

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0044] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present application belongs.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] like Figure 12 As shown, this embodiment provides a method for improving the accuracy of spatial light interferometry technology using a double four-step phase shift method. Based on the theory of partially coherent light, the corresponding Zernike phase contrast microscope imaging formula is derived:

[0047]

[0048] Under the configuration of Olympus phase contrast microscope, the TCC function in the above formula can be well approximated as the result of variable separation.

[0049]

[0050] Depend on Figure 5 The filtering curve in (c) shows that the scattered light is the bandpass filtering result of the object light, and the direct light is the low-pass filtering result of the object light. Figure 5 (d) It can be seen that the low-frequency portion of the approximated TCC error function exhibits a conical distribution. Due to its axial symmetry, the TCC function corresponding to the interference term in Equation 1 does not have an angle function, so the integral result corresponds to a smaller intensity modulated by the four-step phase shift method.

[0051] Furthermore, the technical route of the four-step phase shift method and spatial light interference of the present invention is implemented using the following equations 3 to 7:

[0052]

[0053] a(x)=(I1+I3) / 2+Δn=(I0+I2) / 2+Δn............(4)

[0054] b(x)=(I3-I1) / (4sinφ SLIM )......................................(5)

[0055] φ SLIM =angle((I0-I2)+j(I3-I1))........................(6)

[0056]

[0057] Formula 3 is the calculation model of the four-step phase shift method based on the partially coherent light theory. The error term generated by the approximate cross transfer function TCC of the phase contrast microscope is converted into Equation 2 (see Figure 5(d)) is also modulated by the different phase angles of the four-step phase shift method. Δn in Equation 3 is a random noise term that can include stray light in the system. Calculating the phase angle using Equation 6, while eliminating the TCC approximation error term and the average value of the noise term (system stray light), improves the accuracy of spatial optical interferometry to a certain extent, reducing the relative error by approximately 3% compared to Popescu's calculation method.

[0058] More preferably, the above four-step phase shift method is performed twice, that is, eight images are formed. The first four-step phase shift method is the traditional Popescu four-step phase shift method for measuring the phase of the object. The second four-step phase shift method is displayed on the SLM (liquid crystal spatial light modulator). Figure 6 or Figure 7 grating. Figure 6 The blazed grating directly digs out the edge portion outside the conjugate portion of the ring HL and the ring HS of the light source so that it does not participate in imaging. Figure 7 The phase modulation angles of two adjacent pixels of the mosaic grating are 0° and 180°, so that the edge parts are complex and cancel each other during the TCC integration process.

[0059] Furthermore, in Zernike phase contrast microscopes, this marginal aperture acts as an alignment margin. In practice, this margin can be eliminated by ensuring that the image of the light source ring is aligned with the image of the objective phase plate and the SLM ring on the conjugate plane of the phase plate, the SLM. This minimizes the HL size. Further reduction of the HL to a size smaller than the light source will alter not only the reference light but also the scattered light, rendering the double four-step phase shifting method ineffective.

[0060] Furthermore, since the light source and phase plate dimensions of phase contrast microscopes are already well optimized during their design, and the system requires sufficient light intensity to provide illumination, further reduction in light source size is not recommended. Therefore, the above method represents a significant improvement to Popescu's spatial interferometry technique based on Zernike phase contrast microscopes.

[0061] Examples of microsphere reconstruction using the double four-step phase shifting method:

[0062] In quantitative phase imaging, polystyrene microspheres (n=1.59) and objective oil (n=1.518) are often used to simulate cells. The difference in the internal and external refractive index of polystyrene microspheres is close to that of cells. Figure 8 (a) is an image of a pair of oil-immersed microspheres captured by a 20x phase contrast objective lens under bright field conditions. Due to the reaction between the polystyrene microspheres and the objective lens oil, the microspheres swell slightly. The actual diameter of the microspheres is calculated to be 8.4 μm by measuring the microsphere image in bright field conditions. Figure 8 (b) is the reconstructed three-dimensional phase distribution diagram of the double four-step phase shift method.

[0063] Furthermore, Figure 9The curves in the figure include the phase contour of the standard microsphere, the Popescu OLY curve of the microsphere phase obtained by Popescu's calculation method, and the two SLIM angles, that is, the angle of scattered light minus the angle of direct light, which are the SLIM OLY curve and the SLIM SK curve respectively.

[0064] Furthermore, Figure 9 The angle Δφ of the reference light is obtained by measuring the angle difference of the SLIM twice. R The top of the curve is about 23°. Combining Equation 8, we get the Double 4 curve, the phase measurement calculation result of the double four-step phase shift method. That is, the spatial light interference technology of the double four-step phase shift method eliminates the 23° reference light angle. At this time, the error measured by the spatial light interference technology is given by φ R1 Convert to a smaller φ R2 .

[0065]

[0066] Furthermore, the phase profile reconstructed using the spatial light interferometry technique of the double four-step phase shift method is consistent with the spherical phase. Therefore, it can be determined that the microspheres are dispersed in the objective oil and expand but not deform, and the actual refractive index difference between the inside and outside of the microspheres is 0.0583.

[0067] Furthermore, Figure 10 This is the simulation result based on partial coherence theory. As can be seen from the figure, the angle of the reference light is about -34.3° at the center of the microsphere. Figure 11 In the second step of the double four-step phase shift simulation, a blazed grating is used to remove the portion of the HL that is larger than the HS, or a mosaic is used to eliminate this portion's contribution to the TCC. At this point, the reference beam angle at the microsphere center is approximately -12.9°. The difference between the two is 21.4°, which is consistent with the reference beam angle difference measured by spatial interferometry using the double four-step phase shift method.

[0068] In addition, since the pixel size must satisfy the sampling theorem during simulation, Figure 9 and 10 ,11 have different horizontal scales, but the y-axis direction is the same.

[0069] In summary, for 8.4-micron microspheres, the traditional Popescu spatial interferometry technique measured a relative error of 34.3° / 322.4° = 10.6%. In contrast, the spatial interferometry technique using the dual four-step phase shift method achieved a relative error of 12.9° / 322.4° = 4%, significantly outperforming other quantitative phase imaging techniques.

[0070] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for improving the accuracy of spatial optical interferometry technology using a double four-step phase shift method, characterized in that: The Zernike phase contrast microscope imaging model is obtained using the partially coherent light theory: Among them, I i (x) is the intensity of the i-th phase contrast imaging by the phase shift method; x is the spatial coordinate; I D (x) is the intensity of direct light or reference light; I S (x) is the intensity of scattered light; F(μ) is the spatial frequency distribution of object light; H S (ξ) is the aperture of the light source; H L (μ) is the aperture of the phase ring; H H (μ) is the removal of H L (μ) is the aperture outside; t is the transmittance of the phase plate; Δφ is the modulation angle of the four-step phase shift method; Re is the real part operation; The calculation model adopts the PC-SLIM model, which is a calculation model obtained by studying spatial optical interference technology based on the theory of partially coherent light. It mainly includes the following formulas: a(x)=(I1+I3) / 2+Δn=(I0+I2) / 2+Δn φ SLIM (x)=angle((I0-I2)+j(I3-I1)) f o (x)=φ SLIM (x)+φ R (x),φ Pop (x)=φ H (x)-φ R (x) Among them, I n (x) is the intensity of the phase contrast image obtained by the four-step phase shift method, a(x) = I S (x)+I D (x); Δ(x) is a modulated intensity term obtained by approximating the cross transfer function TCC of the Zernike phase contrast microscope; Δn is the noise of the CMOS or CCD; f(x) is the complex transmittance of the object; where φ SLIM (x) is the angle measurement result of the four-step phase shift method; h S (x) = F -1 (H S (ξ));h H (x) = F -1 (H H (μ));h L (x) = F -1 (H L (μ)); φ o (x) is the phase angle of the complex wave front of the object; φ R (x) is the wavefront angle of the reference light; φ Pop (x) is the phase angle reconstructed by SLIM technology, φ H (x) is the wavefront angle of the scattered light; Perform the four-step phase shift method twice, resulting in eight images. The first four-step phase shift method uses the existing four-step phase shift method to measure the object phase. The second four-step phase shift method uses a mosaic grating or a spectroscopic grating superimposed on the SLM to change the system's cross transfer function (TCC) to measure the object phase. The angle of the scattered light remains unchanged in both measurements, but the reference light angle of the second four-step phase shift method is much smaller than that of the first. The phase is calculated using the following formula: Df R =Df SLIM =φ SLIM1 -f SLIM2 f D4 =φ Pop1 -Df R Among them, φ SLIM1 is the measurement result of the first four-step phase shift method, φ SLIM2 is the measurement result of the second four-step phase shift method, Δφ R is the reference light angle change between the two measurements, φ D4 This is the final calculation result of the SLIM technology using the double four-step phase shift method.

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