23 September 2015 An alternative approach to depth of field which avoids the blur circle and uses the pixel pitch
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Abstract
Modern thermal imaging systems apply more and more uncooled detectors. High volume applications work with detectors which have a reduced pixel count (typical between 200x150 and 640x480). This shrinks the application of modern image treatment procedures like wave front coding. On the other hand side, uncooled detectors demand lenses with fast F-numbers near 1.0. Which are the limits on resolution if the target to analyze changes its distance to the camera system? The aim to implement lens arrangements without any focusing mechanism demands a deeper quantification of the Depth of Field problem. The proposed Depth of Field approach avoids the classic “accepted image blur circle”. It bases on a camera specific depth of focus which is transformed in the object space by paraxial relations. The traditional RAYLEIGH’s -criterion bases on the unaberrated Point Spread Function and delivers a first order relation for the depth of focus. Hence, neither the actual lens resolution neither the detector impact is considered. The camera specific depth of focus respects a lot of camera properties: Lens aberrations at actual F-number, detector size and pixel pitch. The through focus MTF is the base of the camera specific depth of focus. It has a nearly symmetric course around the maximum of sharp imaging. The through focus MTF is considered at detector’s Nyquist frequency. The camera specific depth of focus is this the axial distance in front and behind of sharp image plane where the through focus MTF is <0.25. This camera specific depth of focus is transferred in the object space by paraxial relations. It follows a general applicable Depth of Field diagram which could be applied to lenses realizing a lateral magnification range -0.05…0. Easy to handle formulas are provided between hyperfocal distance and the borders of the Depth of Field in dependence on sharp distances. These relations are in line with the classical Depth of Field-theory. Thermal pictures, taken by different IR-camera cores, illustrate the new approach. The quite often requested graph “MTF versus distance” choses the half Nyquist frequency as reference. The paraxial transfer of the through focus MTF in object space distorts the MTF-curve: hard drop at closer distances than sharp distance, smooth drop at further distances. The formula of a general Diffraction-Limited-Through-Focus-MTF (DLTF) is deducted. Arbitrary detector-lens combinations could be discussed. Free variables in this analysis are waveband, aperture based F-number (lens) and pixel pitch (detector). The DLTF- discussion provides physical limits and technical requirements. The detector development with pixel pitches smaller than captured wavelength in the LWIR-region generates a special challenge for optical design.
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Norbert Schuster, Norbert Schuster, } "An alternative approach to depth of field which avoids the blur circle and uses the pixel pitch", Proc. SPIE 9626, Optical Systems Design 2015: Optical Design and Engineering VI, 96260G (23 September 2015); doi: 10.1117/12.2190769; https://doi.org/10.1117/12.2190769
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