RADIO PHYSICS AND RADIO ASTRONOMY

Subject and Purpose. In this work, the planet surface area relief is calculated using the Improved Photoclinometry Method (IPCM) and starting from a set of source images. Height deviations from the true relief altitudes are studied by computer simulation at small spatial scales (smaller than a quarter of the area’s size). We seek to estimate these "local" errors in surface heights and slopes using source images with different signal-to-noise ratios (SNRs).

Methods and Methodology. The improved photoclinometry method calculates the most probable relief of a planet surface area from its images. Two optional techniques implement this method. The IPCM-F technique employs the optimum Fourier- transform-based fi ltering in the spatial frequency domain. The IPCM-T uses the finite diff erence method to solve the Poisson equation.

Results. Computer experiments on retrieving the surface topography from the source images have shown that the higher the signal-to-noise ratio (SNR) of the initial image, the smaller the size of small-scale features that are reliably reproduced in shape. In the calculations by the IPCM-T technique, the smallest reliably reproduced features are four times the initial image resolution G at SNR ≥ 50 and five times at SNR = 10. With the IPCM-F, the relief features are reliably reproduced starting from spatial scales 9G (SNR ≥ 50) and 17G (SNR ≥ 10). With the IPCM-T, the worst local height error characterizing the smallest reliably reproduced surface features is 0.35σ₀ (SNR = 1) and 0.17σ₀ (SNR = 50), where σ₀is the root-mean-square deviation of the modeled relief height. For both IPCM implementations, larger topographic objects are characterized by local height errors 0.01σ₀ to 0.08σ₀ (SNR = 50).

Conclusions. It has been shown that the surface topography retrieval by the improved photoclinometry method from a set of images with SNR ≥ 50 reliably reproduces shapes of size features ≥ 4G (IPCM-T) and ≥ 9G (IPCM-F). For 8G to 64G size features, the retrieved height local errors are 0.004σ₀ to 0.07σ₀ (IPCM–T) and 0.01σ₀ to 0.08σ₀ (IPCM–F). To study smaller, 4G to 8G size features, the topography relief should be reconstructed using the IPCM-F upon the finite diff erence method.

Keywords: optimal filtering, height calculation error, planetary surface relief, photometry

Manuscript submitted  13.09.2024

Radio phys. radio astron. 2025, 30(1): 024-040

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