An alternative approach to Depth of Field which avoids the blur circle and uses the pixel pitch

摘要

More and more, modern thermal imaging systems now use uncooled detectors. For high volume applications detectors which have a reduced pixel count (typical between 200×150 and 640×480) are normally chosen. This reduces the usefulness of modern image manipulation processes such as wave front coding. On the other hand, uncooled detectors, due to their lower sensitivity, require lenses with fast F-numbers, around f/1.0. What limits the system resolution if the distance from the camera to the target is variable? The frequent requirement to implement a lens solution without a focusing mechanism requires us to have a better understanding of the meaning of the Depth of Field and also a better means to quantify it. The Depth of Field approach proposed here avoids the classical "accepted image blur circle". The new approach is based on a camera specific depth of focus, which is transformed to the object space using paraxial relations. The classical approach uses the Rayleigh λ/4 criterion and is based on the un-aberrated Point Spread Function. This gives a first order relationship to calculate the depth of focus that considers neither the actual lens resolution nor the detector. The camera specific depth of focus proposed uses the properties of the camera, lens aberrations at the used F/Number, detector size and pixel pitch. The through focus MTF is the basis of the camera specific depth of focus, and is considered at the Nyquist frequency of the detector. Usefully, it is nearly symmetrical around the maximum MTF, where the image is sharpest. The depth of focus is defined as the region in front and behind maximum MTF where MTF ＞ 0.25. Having defined the camera specific depth of focus in image space it is necessary to transform this to object space, which is done using the paraxial equations. A generally applicable Depth of Field diagram is developed which can be used for lenses with a lateral magnification in the range -0.05 to 0. Simple formulae are provided that link the hyperfocal distance and the borders of the Depth of Field for variable focus distances. These relationships are in line with the classical Depth of Field theory and thermal pictures, taken using different IR-camera cores, are used to illustrate the new approach. The "MTF versus distance" graph is given with the frequency chosen to be half the Nyquist limit. It is shown that the paraxial transfer of the through focus MTF to object space distorts the MTF curve. It can be seen that there is a fast drop in MTF for object closer that the sharp focus position, while there is a smoother drop for objects further away. The formula for a general Diffraction Limited Through Focus MTF (DLTF) is derived. Several combinations of detector and lens are analyzed. The variables in this analysis are the waveband, aperture based Fumber of the lens and the pixel pitch of the detector. The DLTF discussion provides the physical limits for a given scenario and can help to define the technical requirements. The latest detector developments in the LWIR region, with pixel pitches smaller than the wavelength of the light detected, is particularly challenging for the optical designer.