1 November 1990 Object reconstruction with intensity correlations: signal-to-noise ratio calculation
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Second-, third-, and fourth-order intensity correlations measured in the field in the pupil plane are used to construct the amplitude and phase of the two-dimensional mutual coherence function. Information about the noncoherent object is derived by a two-dimensional spatial Fourier transform of the mutual coherence function. A computer simulation of the Fourier domain laser speckle patterns is used to provide data from which the expected second-, third-, and fourth-order intensity correlations are computed. These correlations are used in the program for the explicit reconstruction of the phase. In addition, the signal-to-noise ratio (SNR) is discussed with reference to the measured integrated intensity, ?0TI(t)dt, as compared to the theoretically assumed instantaneous intensity,I(t). The study of the SNR for the second-, third-, and fourth-order intensity correlations involves higher-order intensity correlations. With the assumed Gaussian statistics of the wave amplitude, the analytical expressions for the higher-order correlations are algebraically complex. The SNR for the third-order case is discussed. For further development, symbolic manipulation programs (e.g., DERIVE, MATHEMATICA, or MACSYMA) will be used. The discussion of the signal-to-noise ratio applies to intensity correlation interferometry (low light levels) for which the integration time, T, is large compared to the coherence time, ?c, that is, T >> ?c. We will consider the case for laser speckle interferometry for which ?c » T in our follow-up work.
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Yiping Z. Hu, Yiping Z. Hu, Arvind S. Marathay, Arvind S. Marathay, Paul S. Idell, Paul S. Idell, "Object reconstruction with intensity correlations: signal-to-noise ratio calculation", Proc. SPIE 1351, Digital Image Synthesis and Inverse Optics, (1 November 1990); doi: 10.1117/12.23668; https://doi.org/10.1117/12.23668

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