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A rigorous and simple method for the determination of the modulation transfer function (MTF) of a sampled imaging system is presented. One calculates the MTF by imaging bar patterns and calculating the reduction in amplitude of the fundamental frequency components. The optimal set of bar-pattern frequencies that reduce errors from aliased frequency components is derived. Theoretical and experimental data are presented.

Streibl [Optik 66, 341-354 (1984)] has shown that afocal telecentric imaging systems are shift invariant in three dimensions. We show that afocal telecentric imaging systems are the only imaging systems that are shift invariant in three dimensions. In addition, we present a model that allows any imaging system to be modeled as an afocal telecentric imaging system preceded and succeeded by simple coordinate transformation operators. The model is derived for diffraction-limited imaging systems where the Fresnel approximation is valid. It is assumed that the object distribution is incoherently radiating and that multiple scattering and absorption within the object distribution are negligible. A physical analogy is given that provides insight into the mathematical model. Finally, a comparison with the work of Frieden is given.

A photospectrometer has been realized in a standard integrated circuit (IC) process. Only the masks, materials, and fabrication steps inherent to this IC process were used (i.e., no post processing to add mechanical or optical devices for filtering). The spectrometer was composed of a set of 18 photodetectors with independent spectral responses. The responses of these devices were weighted and summed to form outputs proportional to the input optical power in discrete wavelength bands in the region from ∼400 to ∼1100 nm. With the solution space restricted to a 60 nm band, this instrument could resolve Gaussian input spectra (σ=5 nm) with a peak-to-peak spacing of less than 15 nm. This device could easily be integrated with additional analog, digital, or wireless circuits to realize a true laboratory instrument on-a-chip.

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