An absolute measurement method for the phase of the object-light complex coherence coefficient

Abstract

This invention proposes a method for absolute measurement of the phase of the complex coherence coefficient of object light. This method first processes fringe data obtained from interferometric measurements of arbitrary apertures on the equivalent pupil plane of an optical system to obtain the interference terms of the interference fringe curve, its envelope, and its extrema. Secondly, for any light intensity maximum A within the relatively stable region of extremal variation on one side of the curve envelope with zero optical path difference, the two extremal intensity values ​​B and C closest to A on the other side of zero optical path difference are selected, satisfying the relationship B>A≥C. Thirdly, the number of fringe periods between A and C is calculated. Finally, based on the number of fringe periods, a formula is selected to calculate the absolute phase of the measured signal. This method is simple in principle, unaffected by the instrument's external environment, and has a wide range of applicability.

Description

Technical Field

[0001] The invention belongs to the field of photoelectric imaging, and provides an absolute measurement method for the phase of the object-light complex coherence coefficient for optical pupil interferometric computational imaging technology. Background Art

[0002] Optical pupil interferometry computational imaging technology has obvious technical advantages in the field of high-resolution imaging, and its equivalent aperture expansion capability is strong. The theory of optical pupil interferometry computational imaging is the Van Set-Zernike law. The complex coherence coefficient μ(u, v) of the object light at the equivalent pupil plane of the optical system is the normalized Fourier transform of the incoherent extended light source distribution I(ξ, η), where (u, v) is the spatial spectrum coordinate, and (ξ, η) is the spatial coordinate of the extended light source. If the complex coherence coefficient μ(u, v) of the light source can be measured, that is, the Fourier spectrum of the light source is obtained, the light source intensity distribution I(ξ, η) can be obtained by inverse Fourier transform. The complex coherence coefficient μ(u, v) includes the modulus |μ| and the phase φ (also known as the amplitude angle), which can be expressed as μ=|μ|e jφ , in theory, can be measured by the interference visibility between the baseline aperture pair and the phase difference at zero optical path.

[0003] Based on this imaging theory, several large-scale interferometers have been built and planned internationally. Currently operating ground-based large-scale optical interferometers include the European Southern Observatory's Very Large Telescope (VLTI), with its longest baseline reaching 200 meters; the U.S. Navy Precision Optical Interferometer (NPOI), with a baseline length of 10-432 meters; and the Center for High Angular Resolution Astronomy (CHARA), with a baseline length of 34-331 meters. Drawing on the technical framework of ground-based astronomical interferometers, NASA and the European Space Agency (ESA) pioneered the free-flyer interferometer program. The Space Interferometry Mission (SIM) was originally intended to be the first space-based long-baseline optical interferometer for astronomical observations. Its astronomical precision was expected to far exceed the capabilities of any other existing or under development projects. Research on this project has been ongoing for many years, but the cancellation of the SIM mission has cast doubt on the development of large-scale space-based interferometers.

[0004] One of the current challenges in the engineering application of large-scale long-baseline interferometers is measuring the complex coherence phase. Astronomical interferometers often use channeled spectrum to disperse a broadband optical signal and record it with an imaging detector. The number of fringes at different optical path differences is used to determine the location of zero optical path difference, thereby achieving complex coherence phase measurement. However, in complex space environments, at scales of tens, tens, or even hundreds of meters, the truss is affected by vibration, heat, and gravity gradients, causing deformation. This can cause the pre-calibrated zero optical path difference position to drift, resulting in a loss of reference. During operation, the instrument must be repeatedly calibrated using reference targets. In addition to channeled spectrum, a closed phase measurement method is also commonly used in astronomical interferometry. Three relative phases are obtained by pairing three apertures in pairs. While this method can theoretically eliminate the effects of atmospheric turbulence, the number of closed phases is always smaller than the true phase, requiring the development of a specific algorithm to determine the true complex coherence phase. When complex coherence phase measurement is unavailable, scientists attempt to iteratively optimize algorithms to recover the complex coherence phase and reconstruct high-resolution images.

[0005] To address the measurement challenges of the complex coherence coefficient phase in optical pupil interferometry imaging systems and advance the engineering application of this imaging technology, the present invention proposes a method for measuring the absolute value of the complex coherence coefficient phase by comparing the interference extremes on both sides of the interference envelope. This method is simple in principle, unaffected by the instrument's external environment, and has a wide range of applications. Compared to the invention patent for a relative measurement method of the complex coherence coefficient phase (Application Number: 2023103687876), this method is simpler to operate and has higher measurement efficiency. Summary of the Invention

[0006] Expanding on the Van Cittert-Zernike theorem, the mutual interference function of the optical signals received by the two endpoints P1 and P2 of any baseline on the equivalent pupil surface of the optical system can be described by the following formula:

[0007]

[0008] Where,

[0009]

[0010]

[0011] I(P1) and I(P2) are the light intensities of the optical signals received at P1 and P2, respectively. γ(P1, P2, τ) is the complex coherence of the optical signals at P1 and P2 when the time delay is τ. I(α, β, v) is the extended light source at the object plane (α, β) in the frequency band. The light intensity per unit area, R1 and R2 are the distances from the light source I(α, β, v) to P1 and P2 respectively.

[0012] When τ = 0, the complex coherence of the optical signal at P1 and P2 can be obtained from (1)

[0013]

[0014] Assuming a narrowband frequency band The light source intensity I(α, β, v) of each frequency in the same element within the light source area D is the same, and the complex coherence can be expressed as the modulus G and phase of the complex coherence coefficient μ(u, v) (also called argument) form, that is,

[0015]

[0016] Substituting equation (5) into equation (1) and taking into account the spectral response function T(v) of the imaging system, the complex coherence degree obtained after the optical signal is transmitted through the coupler is:

[0017]

[0018] Assuming that the total dispersion of the optical signal in all media is 0, then

[0019]

[0020] Where F(τ) is the Fourier transform of the function T(v), F(τ)=|F(τ)|e if(τ) ; f(τ) is a phase term related to the spectral shape. In particular, when T(v) is symmetric about the center frequency v0, F(τ) is a real function, f(τ) = 0 or π. F0 can be regarded as a constant.

[0021] Therefore, the interference fringes generated by the coupler for the light signal received by the corresponding aperture at the two end points P1 and P2 of any baseline on the equivalent pupil plane of the optical system can be expressed as:

[0022]

[0023] Where I(P1)' and I(P2)' represent the light intensities of the optical signals at P1 and P2 respectively after being split by the imaging system.

[0024] Among them, the interference term is a constant, let |F(τ)| can be regarded as the envelope function of the interference fringes. When I Δ (τ) is the maximum value (n∈N), when When I Δ (τ) is the minimum value.

[0025] Assume that T(v) is symmetric about the center frequency v0, and that f(τ) = 0 within the main lobe containing the zero optical path difference position. For an object light signal with a phase of φ, when τ is in the range where the first-order derivative of |F(τ)|, |F(τ)|' = k, is approximately constant and the second-order derivative is close to zero, that is, take any maximum intensity value within the range where the extreme value change of the interference signal in the main lobe on the zero optical path side of the interference signal is relatively stable. (n is an integer).

[0026] When 0≤φ<π, in the main lobe on the other side of the zero optical path difference, the extreme light intensity value closest to the complex coherence factor is and and at this time and There are an even number of fringe periods between them. The phase φ of the measured signal satisfies the relationship:

[0027]

[0028] When π≤φ<2π, in the main lobe on the other side of the zero optical path difference, the extreme light intensity value closest to the complex coherence factor is and And there is at this time and There are an odd number of fringe periods between them. The phase φ of the measured signal satisfies the relationship:

[0029]

[0030] In summary, we only need to accurately measure a light intensity maximum or minimum point on one side of the zero optical path difference, and the two closest light intensity maximum points on the other side, and compare the maximum values ​​based on the number of fringe periods between these maximum points to calculate the phase φ of the complex coherence coefficient corresponding to the interference signal. The steps for the absolute measurement method of the complex correlation coefficient phase are as follows:

[0031] Step 1: Obtain interference fringes by interferometric coupling of the light signals received by the corresponding aperture pair at the two end points P1 and P2 of any baseline on the equivalent pupil surface of the optical system;

[0032] Step 2: Remove DC and noise from the interference fringe signal to obtain the interference fringe interference term curve, as well as its envelope and extreme values;

[0033] Step 3: For any maximum light intensity value A within the relatively stable interval of the maximum value change of the interference signal in the main lobe on the zero optical path side of the interference fringe, select the two extreme light intensity values ​​B and C closest to the extreme value A within the relatively stable interval of the maximum value change of the interference signal in the main lobe on the other side of the zero optical path, and satisfy the relationship B>A≥C;

[0034] Step 4: Calculate the number of fringe periods between A and C;

[0035] Step 5: When the number of fringe periods is even, calculate the absolute phase of the measured signal

[0036] Step 6: When the number of fringe periods is odd, calculate the absolute phase of the measured signal

[0037] Based on the same principle, the absolute phase difference of the measured signal can also be calculated by comparing the minimum values ​​in the interference fringe curve. The specific method steps are as follows:

[0038] Step 1: Obtain interference fringes by interferometric coupling of the light signals received by the corresponding aperture pair at the two end points P1 and P2 of any baseline on the equivalent pupil surface of the optical system;

[0039] Step 2: Remove DC and noise from the interference fringe signal to obtain the interference fringe interference term curve, as well as its envelope and extreme values;

[0040] Step 3: For any light intensity minimum value A within the interval where the interference signal minimum value changes relatively stably in the main lobe on the zero optical path side of the interference fringe, select the two extreme light intensity values ​​B and C closest to the extreme value A within the interval where the interference signal maximum value changes relatively stably in the main lobe on the other side of the zero optical path, and satisfy the relationship C>A≥B;

[0041] Step 4: Calculate the number of fringe periods between A and C;

[0042] Step 5: When the number of fringe periods is odd, calculate the absolute phase of the measured signal

[0043] Step 6: When the number of fringe periods is even, calculate the absolute phase of the measured signal BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 : Absolute measurement method of the phase of the object-light complex coherence coefficient.

[0045] Figure 2 : Optical path layout diagram of the phase of the target to be measured in aperture interferometry test.

[0046] Figure 3 : Target pattern to be measured.

[0047] Figure 4 : Simulation diagram of interference fringes without dispersion effect.

[0048] Figure 5: The change of the calculated phase value of the target to be measured with the position of the extreme value when there is no dispersion influence.

[0049] Figure 6 : Simulation diagram of interference fringes with dispersion effect.

[0050] Figure 7 : The change of the phase calculation value of the target to be measured with the position of the extreme value when there is dispersion influence. DETAILED DESCRIPTION

[0051] Example: Phase measurement of a target using aperture interferometry

[0052] The simulation measurement optical path layout is as follows Figure 2 As shown in the figure, the extended light source passes through the target and enters the collimator for collimation before being output. It is collected by a pair of apertures with specific spacing, and then enters the 2×1 coupler for interference after passing through the optical fiber and the fiber delay. The interference signal is then recorded by the optical power meter. During the measurement, the fiber delay is adjusted by computer control while the interference signal is collected and recorded. The target is a black and white periodic stripe pattern with a period of 50 microns, as shown in the figure. Figure 3 As shown, the collimator has a focal length of 2260 mm and a center-to-center distance of 75 mm between the two apertures. Before testing, the target position is adjusted so that the apertures are symmetrical about the center axis of the pattern in the field of view, which is recorded as the target zero position. The target light source is turned on, and the fiber retarder is adjusted so that it sweeps through the zero optical path difference between the two optical paths, and the interference data is measured and recorded. The target is then translated in 2.5-micron steps, and the fiber retarder is repeatedly adjusted so that it sweeps through the zero optical path difference between the two optical paths, and the interference data is measured and recorded. The collected raw data is filtered to remove DC and calculate the interference term, which is then normalized to determine the interference term intensity.

[0053] Assuming that the optical path has no dispersion effect, the interference term intensity curve after DC normalization in the simulation test is as follows: Figure 4 As shown in the figure, according to the interference fringe envelope extreme value method disclosed above, the phase values ​​of the target to be measured are calculated when the target is located at 2.5 microns, 7.5 microns, 12.5 microns, 17.5 microns, and 22.5 microns. The theoretical phase values ​​should be 0.1π, 0.3π, 0.5π, 0.7π, and 0.9π respectively. The simulation shows that when the maximum value A is located at different positions of the optical path difference, the phase values ​​of the target to be measured obtained by measurement and calculation are slightly different, as shown in the figure. Figure 5 shown.

[0054] Assuming the presence of dispersion, a spectral response function is added to the simulation, and the DC-normalized interference term intensity curve is as follows: Figure 6As shown, according to the method of the interference fringe envelope extreme value disclosed above, the phase values ​​of the target to be measured when it is located at 2.5 microns, 7.5 microns, 12.5 microns, 17.5 microns and 22.5 microns are calculated. The theoretical phase values ​​should be 0.1π, 0.3π, 0.5π, 0.7π, and 0.9π respectively. Simulation shows that due to the influence of optical path dispersion, the accuracy of the phase value of the target to be measured obtained by measurement and calculation is related to the position of the maximum value A at the distance from zero optical path difference, that is, it is affected by the relative stability of the extreme value change. The phase test accuracy is slightly worse than the measurement result without dispersion, such as Figure 7 This problem can be solved by calibration before measurement. That is, before measuring the phase of the target to be measured, the phase of a standard target can be measured to determine the extreme value in the optical path difference range with smaller measurement error, thereby guiding the subsequent measurement and data processing of the target phase.

[0055] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent method or process transformation made by using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for absolute measurement of the phase of the object-light complex coherence coefficient, characterized by: (1) Comparison of the maximum value of interference terms of interference fringes is performed as follows: Step 1: Obtain interference fringes by interferometric coupling of the light signals received by the corresponding aperture pair at the two end points P1 and P2 of any baseline on the equivalent pupil surface of the optical system; Step 2: Remove DC and noise from the interference fringe signal to obtain the interference fringe interference term curve, as well as its envelope and extreme values; Step 3: For any maximum light intensity value A within the relatively stable interval of the maximum value change of the interference signal in the main lobe on the zero optical path side of the interference fringe, select the two extreme light intensity values ​​B and C closest to the maximum value A within the relatively stable interval of the maximum value change of the interference signal in the main lobe on the other side of the zero optical path, and satisfy the relationship B>A≥C; Step 4: Calculate the number of fringe periods between A and C; Step 5: When the number of fringe periods is even, calculate the absolute phase of the measured signal Step 6: When the number of fringe periods is odd, calculate the absolute phase of the measured signal (2) Comparison of the minimum value of the interference term of the interference fringes is performed as follows: Step 1: Obtain interference fringes by interferometric coupling of the light signals received by the corresponding aperture pair at the two end points P1 and P2 of any baseline on the equivalent pupil surface of the optical system; Step 2: Remove DC and noise from the interference fringe signal to obtain the interference fringe interference term curve, as well as its envelope and extreme values; Step 3: For any light intensity minimum A within the interval where the interference signal minimum value changes relatively stably in the main lobe on the zero optical path side of the interference fringe, select the two extreme light intensity values ​​B and C closest to the minimum value A within the interval where the interference signal maximum value changes relatively stably in the main lobe on the other side of the zero optical path, and satisfy the relationship C>A≥B; Step 4: Calculate the number of fringe periods between A and C; Step 5: When the number of fringe periods is odd, calculate the absolute phase of the measured signal Step 6: When the number of fringe periods is even, calculate the absolute phase of the measured signal

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