Line spread function formulation proposed by W. H. Steel: a revision.
A revised formulation of the image light distribution of an incoherent line source proposed by Steel [Rev. Opt. 31, 334-340 (1952)] is presented. Analytical and numerical results based on this new representation are given. We explicitly show that a major error in Steel's final expression generates singularities, thereby preventing convenient numerical computation.
Introduction To The Optical Transfer Function
This work covers spatial frequency, spread function, wave aberration, and transfer function - and how these concepts are related in an optical system, how they are measured and calculated, and how they may be useful.
Characteristics of an image-forming system
For the past few ." ears considerable energy has been expended in the searcb for an objective procedure for evalua ting the qualit,y of imnges formed by optical instrumen Ls. Existing procedures have been found to be not entirely satisfactory, and much " 'ork has been done in measuring previously unused physical parameters, which arc objectively determinnble, for the purpose of correlating them with the exieting quality cri teria. The objection to Lhis is that such an empirical, and therefore much limi ted, correlation eliminates only one of Lhe faults of the existing criteria, and this is the SUbj ectivity of tbeir determination. Any other weakne s is ignored. A better approach is Lo analyze Lhe imao'e-forming process as a phenomenon , the aim being to characterize the process in as general and in elusive a way as possible, consistent with practical instmmentatioll. Ke\\' criLeria of image quality would of course be expected to be developed . Many approaches hnve been made in this direction also, and lhe present paper is to be included among them. However, in co ntrast to some of the published material, the emphasis here is on the practicali ty and usefulness of the result obtained rat.her than on mathematical rigor, although the treatme nt should be rigorous enough to include all essenlial factors. Let us consider this matter oJ practical instrumentation. The heart of the test in lmment is the photosensitive detector, for it is this which provides the data by which the tested instrument is eval uaLed. Three practi cal photosrnsitive detectors are available-the eye, the photographic emulsion , and the pholocell. The only test of image quality for which the eye is capable of making quanLiLative measureme nts is the resolving-power test. Thi s Lest is rapid and relatively inexpensive, but. the information obUtined i incornplete, the precision is low, and the results are ubjecL to variation from individual to indi vidual. A photographic detector allows quantitative measLirements to be mnde under nonthreshold conditions, but lime is required £or processing, the proce sing condilions mu t be rigidly standardized, the granularity and difi"usion in the emulsion affect the results, t he response of lbe film is nonlinear with respect to incident Jlux, and, in tbe end, an additional sensing mechani m, such as a microdensitometer, is needed to reduce the emulsion properties Lo nUlllerical alues. The photocell is probably t he most satisfactory photosensitive detector for the test instmment. 'Within its proper operating range, its characteristics remain reasonably constant, iLs response is linear with respect to incident flux, its spectral response can be adjusted so as to approximate that of the e." e, and its oUlput can very easily produce graphical or numerical results. However, it must be used in conjunction with an aperture that limits the spatial integration of the detail in lhe image being examined, and there must be provision for relative di splacement between the aperture and the image so that various portions of the image may be sampled. It hould also be pointed out that the report is illustrated throughout by the characteristics of an aberration-free ystem with a circular aperture in monochromatic light, diffraction being the sole source of image degradation, and the light from various points in the object space being noncoherent. This has been selected as an interesting and informative type of system, which real systems tend to approximate as their quali ty improves. It mu t be empba ized,