17 May 2016 Evaluate depth of field limits of fixed focus lens arrangements in thermal infrared
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Abstract
More and more modern thermal imaging systems use uncooled detectors. High volume applications work with detectors that have a reduced pixel count (typically between 200x150 and 640x480). This reduces the usefulness of modern image treatment procedures such as wave front coding. On the other hand, uncooled detectors demand lenses with fast fnumbers, near f/1.0, which reduces the expected Depth of Field (DoF). What are the limits on resolution if the target changes distance to the camera system? The desire to implement lens arrangements without a focusing mechanism demands a deeper quantification of the DoF problem. A new approach avoids the classic “accepted image blur circle” and quantifies the expected DoF by the Through Focus MTF of the lens. This function is defined for a certain spatial frequency that provides a straightforward relation to the pixel pitch of imaging device. A certain minimum MTF-level is necessary so that the complete thermal imaging system can realize its basic functions, such as recognition or detection of specified targets. Very often, this technical tradeoff is approved with a certain lens. But what is the impact of changing the lens for one with a different focal length? Narrow field lenses, which give more details of targets in longer distances, tighten the DoF problem. A first orientation is given by the hyperfocal distance. It depends in a square relation on the focal length and in a linear relation on the through focus MTF of the lens. The analysis of these relations shows the contradicting requirements between higher thermal and spatial resolution, faster f-number and desired DoF. Furthermore, the hyperfocal distance defines the DoF-borders. Their relation between is such as the first order imaging formulas. A calculation methodology will be presented to transfer DoF-results from an approved combination lens and camera to another lens in combination with the initial camera. Necessary input for this prediction is the accepted DoF of the initial combination and the through focus MTFs of both lenses. The accepted DoF of the initial combination defines an application and camera related MTF-level, which must be provided also by the new lens. Examples are provided. The formula of the Diffraction-Limited-Through-Focus-MTF (DLTF) quantifies the physical limit and works without any ray trace. This relation respects the pixel pitch, the waveband and the aperture based f-number, but is independent of detector size. The DLTF has a steeper slope than the ray traced Through-Focus-MTF; its maximum is the diffraction limit. The DLTF predicts the DoF-relations quite precisely. Differences to ray trace results are discussed. Last calculations with modern detectors show that a static chosen MTF-level doesn’t reflect the reality for the DoFproblem. The MTF-level to respect depends on application, pixel pitch, IR-camera and image treatment. A value of 0.250 at the detector Nyquist frequency seems to be a reasonable starting point for uncooled FPAs with 17μm pixel pitch.
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Norbert Schuster, Norbert Schuster, } "Evaluate depth of field limits of fixed focus lens arrangements in thermal infrared", Proc. SPIE 9822, Advanced Optics for Defense Applications: UV through LWIR, 98220G (17 May 2016); doi: 10.1117/12.2223559; https://doi.org/10.1117/12.2223559
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