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Optical phase-modulated fringe-patterns are usually digitized with XxY pixelsand 8 bits/pixel (or higher) gray-levels. The digitized 8 bits/pixel areraw-data bits, not Shannon information bits. Here we show that noisyfringe-patterns store much less Shannon information than the capacity of thedigitizing camera. This means that high signal-to-noise ratio (S/N) cameras maywaste to noise most bits/pixel. For example one would not use smartphonecameras for high quality phase-metrology, because of their lower (S/N) images.However smartphones digitize high-resolution (12 megapixel) images, and as weshow here, the information storage of an image depends on its bandwidth and its(S/N). The standard formalism for measuring information are the Shannon-entropyH, and the Shannon capacity theorem (SCT). According to SCT, low (S/N) imagesmay be compensated with a larger fringe-bandwidth to obtain high-informationphase measurements. So broad bandwidth fringes may give high quality phase, inspite of digitizing low (S/N) fringe images. Most real-life images areredundant, they have smooth zones where the pixel-value do not change much, anddata compression algorithms are paramount for image transmission/storage.Shannon's capacity theorem is used to gauge competing image compressionalgorithms. Here we show that phase-modulated phase-shifted fringes are highlycorrelated, and as a consequence, phase-shifting algorithms (PSAs) may be usedas fringe-data compressors. Therefore a PSA may compress a large number ofphase-shifted fringes into a single complex-valued image. This is important inspaceborne optical/RADAR phase-telemetry where downlink is severely limited byhuge distance and low-power downlink. That is, instead of transmitting Mphase-shifted fringes, one only transmit the phase-demodulated signal ascompressed sensing data.

Shannon information storage in noisy phase-modulated fringes and fringe-data compression by phase-shifting algorithms