A Theory of Scanning and Its Relation to the Characteristics 



of the Transmitted Signal in Telephotography and 



Television 



By PIERRE MERTZ and FRANK GRAY 



By the use of a two-dimensional Fourier analysis of the transmitted 

 picture a theory of scanning is developed and the scanning system related 

 to the signal used for the transmission. On the basis of this theory a 

 number of conclusions can be drawn: 



1 . The result of the complete process of transmission may be divided into 

 two parts, (a) a reproduction of the original picture with a blurring similar 

 to that caused in general by an optical system of only finite perfection, and 

 (6) the superposition on it of an extraneous pattern not present in the 

 original, but which is a function of both the original and the scanning 

 system. 



2. Roughly half the frequency range occupied by the transmitted 

 signal is idle. Its frequency spectrum consists of alternating strong bands 

 and regions of weak energy. In the latter the signal energy reproducing 

 the original is at its weakest, and gives rise to the strongest part of the 

 extraneous pattern. In a television system these idle regions are several 

 hundred to several thousand cycles wide and have actually been used 

 experimentally as the transmission path for independent signaling channels, 

 without any visible effect on the received picture. 



3. With respect to the blurring of the original all reasonable shapes of 

 aperture give about the same result when of equivalent size. The sizes 

 (along a given dimension) are determined as equivalent when the apertures 

 have the same radius of gyration (about a perpendicular axis in the plane 

 of the aperture). 



4. With respect to extraneous patterns certain shapes of aperture are 

 better than others, but all apertures can be made to suppress them at the 

 expense of blurring. An aperture arrangement is presented which almost 

 completely eliminates extraneous pattern while about doubling the blurring 

 across the direction of scanning as compared with the usual square aperture. 

 From this and other examples the degradation caused by the extraneous 

 patterns is estimated. 



TN the usual telephotographic or television systems the image field 

 •^ is scanned by moving a spot or elementary area along some recurring 

 geometrical path over this field. In the more common arrangement 

 this path consists simply of a series of successive parallel strips. 

 Imagining the path developed or straightened out (or in the more com- 

 mon case, the strips joined end to end), this method of scanning is 

 equivalent to transmitting the image in the form of a long narrow strip. 

 The theoretical treatment of such transmission has usually been 

 developed by completely ignoring variations in brightness across the 

 image strip, assuming the brightness to have a uniform distribution 

 across this strip. This permits the image to be analyzed as an ordin- 

 ary one-dimensional or single Fourier series (or integral) along the 

 length of the strip; and the theory is then developed in terms of the 



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