A method for relative measurement of complex correlation coefficient phase

Abstract

The application provides a relative measurement method of complex coherence coefficient phase, which comprises the following steps: firstly, extracting extreme values in the interference envelope of two measurement data; secondly, selecting two adjacent extreme values and in the relatively stable region of the extreme value change on one side of the first measurement data envelope; thirdly, selecting extreme values between the two adjacent extreme values and on the same side of the first measurement data envelope in the second measurement data; and fourthly, comparing and calculating the phase difference of the two measurement data. The method has simple principle, is not affected by external environment of instruments, and has wide application range.

Description

Technical Field

[0001] This invention belongs to the field of photoelectric imaging and provides a relative measurement method for the phase of complex coherence coefficients in optical interferometric pupil plane computational imaging technology. Background Technology

[0002] Optical pupil plane interferometry computational imaging technology has significant technical advantages in the field of high-resolution imaging, with strong capability for expanding the equivalent aperture. The theory behind optical pupil plane interferometry computational imaging is the van der Zernike law. The object light complex coherence coefficient μ(u, v) 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) are the spatial spectral coordinates, and (ξ, η) are the spatial coordinates of the extended light source. If the complex coherence coefficient μ(u, v) of the light source can be measured, i.e., the Fourier spectrum of the light source is obtained, the intensity distribution I(ξ, η) of the light source can be obtained through the inverse Fourier transform. The complex coherence coefficient μ(u, v) includes the modulus |μ| and the phase φ (also known as the argument), and can be expressed as μ = |μ|e^(-μ|). jφ In theory, it can be determined by the interference visibility between baseline aperture pairs and the phase difference at zero optical path.

[0003] Based on this imaging theory, several large interferometers have been built and planned internationally. Currently operating ground-based large optical interferometers include the Very Large Telescope (VLTI) at the European Southern Observatory, with a baseline of up to 200m; the Navy Precision Optical Interferometer (NPOI) with a baseline of 10-432m; and the Center for High Angular Resolution Astronomy (CHARA) with a baseline of 34-331m. Drawing on the technology 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 planned to be the first long-baseline optical interferometer in space, used for astronomical observations, with the expected accuracy of astronomical measurements far exceeding the capabilities of any existing or under-development projects. Research on this project continued for many years, but the SIM mission has now been cancelled, leaving the development path of large space interferometers shrouded in mystery.

[0004] One of the challenges in the engineering applications of large long-baseline interferometers is the difficulty in measuring the phase of the complex coherence coefficient. Astronomical interferometers commonly use channeled spectroscopy to disperse broadband light signals, which are then recorded by an imaging detector. The location of the zero optical path difference is determined by observing the number of fringes at different optical path differences, thus enabling the measurement of the complex coherence coefficient phase. However, in complex space environments, at scales of tens of meters or even hundreds of meters, the truss is deformed by vibrations, heat, and gravitational gradients, causing the pre-calibrated zero optical path difference position to drift and lose its reference. During operation, the instrument needs repeated calibration using a reference target. Besides channeled spectroscopy, a closed-phase measurement method is also commonly used in astronomical interferometry. This method obtains three sets of relative phases by pairing three apertures. While this method theoretically eliminates the influence of atmospheric turbulence, the number of closed phases is always less than the true phase. Therefore, a specific algorithm is needed to solve for the true complex coherence coefficient phase. When the complex coherence coefficient phase cannot be measured, scientists attempt to iteratively optimize algorithms to recover the complex coherence coefficient phase, thereby reconstructing high-resolution images. Summary of the Invention

[0005] To address the challenge of measuring the phase of complex coherence coefficients in optical pupil plane interferometry computational imaging technology and to advance the engineering application of this imaging technology, this invention proposes a method for measuring the phase of complex coherence coefficients by comparing interferometric extrema. This method is simple in principle, unaffected by the external environment of the instrument, and has a wide range of applications.

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

[0007]

[0008] In the formula,

[0009]

[0010]

[0011] I(P1) and I(P2) are the light intensities of the received optical signals at points P1 and P2, respectively; γ(P1,P2,τ) is the complex coherence of the optical signals at points P1 and P2 with a time delay τ; and I(α,β,v) is the frequency response of the extended light source at the object plane (α,β) in the frequency band. Let R1 and R2 be the light intensity per unit area, and R1 and R2 be 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 signals at P1 and P2 can be obtained from (1).

[0013]

[0014] Assuming in narrowband frequency band Within the light source region D, the light source intensity I(α,β,v) at all frequencies is the same in the same surface element. The complex coherence can be expressed as the modulus G and phase of the complex coherence coefficient μ(u,v). The form, that is

[0015]

[0016] Substituting equation (5) into equation (1), and considering the spectral response T(v) of the imaging system, we can obtain the complex coherence of the optical signal after transmission interference via the coupler as follows:

[0017]

[0018] Assuming the total dispersion of the optical signal is zero during propagation through all media, 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 considered a constant.

[0021] Therefore, the interference fringes generated by the coupler can be represented as:

[0022]

[0023] In the formula, I(P1)' and I(P2)' represent the light intensity of the light signals at P1 and P2 after being split by the imaging system, respectively.

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

[0025] To simplify the analysis, assume that T(v) is symmetric about the center frequency v0, then f(τ) = 0 or π. Further assume that f(τ) corresponds to 0 for both adjacent maxima of the interference fringes. For two interference signals with a phase difference of m, the phase... Let them be denoted as m1 and m2 respectively (0≤m1≤2π, 0≤m2≤2π). When When τ is in the interval where the first derivative of |F(τ)|, |F(τ)|'=k, is approximately constant and the second derivative is close to zero, the extreme value changes stably. The interference signal I Δ The two adjacent maxima are and The interference signal is between and The maximum value between Then the following relationship exists:

[0026]

[0027] Here, m represents the phase difference between the two interference signals m1 and m2, or it can be expressed as the phase deviation of the interference signal with phase m2 relative to the interference signal with phase m1. Similarly, it can also be expressed according to I. Δ The minimum value was calculated Therefore, the interference signal with a phase difference of m satisfies That is, the phase difference between two interference signals can be calculated based on the corresponding two adjacent maxima or minima of the interference signals.

[0028] The method can be summarized as follows: For the target to be measured by aperture-based collection and transmission, the fiber optic delay device is adjusted, i.e., the time delay τ is adjusted, to obtain the interference signal. First, the extreme values ​​within the interference envelope of the two measurements are extracted; second, within the relatively stable region of extreme value changes on one side of the data envelope of the first measurement, two adjacent extreme values ​​are selected. and Furthermore, in the second measurement data, data from the same side as the data network in the first measurement and located between two adjacent extreme values ​​are selected. and extreme values ​​between Finally, the phase difference between the two measurements was calculated by comparison. Attached Figure Description

[0029] Figure 1 This is a block diagram of the phase relative measurement method.

[0030] Figure 2 This is a layout diagram for phase difference testing.

[0031] Figure 3 It is a black-and-white periodic modulation target image.

[0032] Figure 4 This is a graph of two-channel interferometric data measurements. In Figure (a), the normalized interferometric term I is obtained from multiple measurements of one output channel of the coupler. ΔThe absolute value plot of the extreme points; Figure (b) shows the normalized interference term I measured multiple times on the other output channel of the coupler. Δ Absolute value graph of extreme points.

[0033] Figure 5 This is a graph showing the results of the data processing. Detailed Implementation

[0034] Example: Measurement and calculation of the phase difference between two signals.

[0035] Test layout diagram as follows Figure 2 As shown, the extended light source passes through the target, is collimated by a collimator, and then output. It is collected by an aperture pair, passes through an optical fiber and a fiber delayer, and then enters a 2×2 coupler for interference input. Finally, it is recorded by an optical power meter. During the measurement, the interference signal is acquired and recorded simultaneously by adjusting the fiber delayer via a computer. The target is a black and white periodic stripe pattern, as shown... Figure 3 As shown. The target light source is turned on, and the fiber optic retarder is adjusted to sweep across the zero optical path difference position between the two optical paths. Interference envelopes 1 and 2 are measured and recorded using two couplers respectively. The acquired raw data is filtered to calculate the interference term I. Δ Further normalized interference terms are obtained. The absolute value is then selected, and the extreme point of the main lobe on one side of the envelope with relatively stable extreme value changes, that is, the extreme point with a value in the range of [0.5, 0.62], is finally calculated according to formula (9). and The value of is obtained to determine the phase difference between the two interference signals.

[0036] Figure 4 This is a graph of two-channel interferometric data measurements. In Figure (a), the normalized interferometric term I is obtained from multiple measurements of one output channel of the coupler. Δ The absolute value plot of the extreme points; Figure (b) shows the normalized interference term I measured multiple times on the other output channel of the coupler. Δ A graph of the absolute values ​​of extreme points. From... Figure 4 It can be seen that the distribution of multiple measurements of the absolute values ​​of adjacent maxima and minima overlaps to some extent. The symbol 'a' represents the absolute value of the maxima, 'b' represents the absolute value of the minima, 'n' represents the index of the extreme point, and 'm1' and 'm2' represent the interference signal channels of the two phases. Figure 5 It is to utilize Figure 4 The minimum and maximum values ​​shown are calculated as follows and All in the picture The average value is 0.57. The mean is 0.52, and the standard deviation of all data is 0.12. According to... The phase difference between these two channels is calculated to be 1.09π. Since the theoretical phase difference between the two outputs of the 2×2 coupler is π, the measured value differs from the theoretical value by 0.09π.

Claims

1. A method for relative measurement of the phase of a complex coherence coefficient, characterized in that... The method is as follows: First, extract the extreme values ​​within the interference envelope of the two measurements; second, within the relatively stable region of extreme value changes on one side of the data envelope of the first measurement, select two adjacent extreme values. and Furthermore, in the second measurement data, data from the same side as the data network in the first measurement and located between two adjacent extreme values ​​are selected. and extreme values ​​between Finally, the phase difference between the two measurements was calculated by comparison.

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