The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

On the diffraction theory of optical images

This paper describes a change in optical spectrum on propagation in free space for a particular class of spatially partially coherent fields emanating from a polychromatic secondary source. A rectangular opening aperture in an opaque screen, illuminated with an extended incoherent polychromatic primary source, works as the secondary source. The spectral change is explored in detail theoretically and experimentally in association with spatial coherence in the secondary source as well as dispersive diffraction by the secondary source. The peak shift of the spectrum is associated with the coherence area for characterizing the secondary source. The peak shift becomes maximum if the secondary source is spatially coherent, but no shift occurs if the secondary source is spatially incoherent.

Effects of Spatial Coherence and Dispersive Diffraction on a Change in Optical Spectrum

Optical mutual intensity can be controlled by the variable intensity distribution of an extended quasi-monochromatic incoherent source. A point source with a conceptually variable intensity, moving stepwise over the source plane, is capable of providing an equivalent extended incoherent source. This idea can be realized by an opto-electronic hybrid system. The intensity pattern of an object illuminated stepwise by a movable point source with unit intensity is recorded at every step by a CCD TV camera and held in a computer memory. All the memorized intensity patterns are multiplied successively with a series of weighting values from a suitable function generated in the computer. This generated function can take the same formula as the required intensity distribution of an extended incoherent source. The sum total of all the weighted elementary patterns results in an intensity pattern of the object equivalent to that formed by spatially coherence-controllable illumination. The computer-generated image patterns for a knife-edge object are in good agreement with the measured image patterns. The image pattern can be shaped with the help of such a function generated in the computer.

H. Matsubara

Papers

Realization of pseudo-coherence-controllable illumination for shaping the intensity pattern of an object using an opto-electronic hybrid system