Haidinger fringe

Abstract: The utilization of detector arrays in the focal planes of FTS sensor systems allows simultaneous spectral and spatial measurements. However, spectral lineshapes and wavenumber locations depend upon the size and location of the detector elements with respect to the Haidinger fringe pattern of the FTS sensor. These spectral distortions can be generalized as a shift and shape change of the FTS sensor lineshape. Depending on the distortions that can be tolerated, a degree of field-widening can be obtained for a given Haidinger fringe pattern. An exact model for predicting the FTS lineshape distortions is presented. The model is applied to several contemporary applications in order to quantify the magnitude of distortions to be expected.

Abstract: The increasing use of detector arrays in Fourier Transform Spectroscopy requires an understanding of the line shape spectral shifts and distortions inherent in using off-axis sensors. For rectangular, sector, and circular shaped detectors a compact formulation is presented for calculating these factors without the necessity for numerical modeling.1. SUMMARYThe use of mosiac detector arrays in the focal planes of Michelson interferometers has prompted interest in the spectral line shape functions for detectors placed beyond the usual on-axis position within the first Haidinger fringe. Beginning with the paper by 4 Guelachvili2 for off-axis circular detectors, and the work of Niple, et al3 and Yapp et al, a qualitative view of the spectral distortions expected for various shaped off-axis detectors was achieved after considerable numerical modeling.*'"''However, it appears that quantitative formulae can be given for the rectangular, sector, and circular off-axis detectors which represent the line shape functions in terms of compact inverse trigometric functions, and which are useful for quickly determining these factors for optimization studies, for example in using focal planes arrays in field- widening applications.Because of the variation of optical path length difference between the two beams of a Michelson interferometer for off-axis rays, a finite size detector in the focal plane responds to the spatial average of the Haidinger fringe pattern over the solid angle subtended by the detector. For a particular wave number ao, and for small off-axis angles, this requires the evaluation of the integral

Abstract: PROF. S. TOLANSKY1 has made some comments on communications by Bruce2 and Bruce, Macinante and Kelly3 on the production and applications of transmissionlike reflexion fringes. I am grateful for the reference to the paper by Lummer4 in which the principle of eliminating beams in a Haidinger fringe system is mentioned.