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ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 28B Advances in Electronics and Electron Physics EDITED BY L. MARTON National Bureau of Standards, Washington, D.C. Assistant Editor CLAIREMARTON EDITORIAL BOARD M. Ponte T. E. Allibone H. B. G. Casimir W. G. Dow A. 0. C. Nier E. R. Piore A. Rose L. P. Smith I?. I 1/(2P,)and a < 1/(2fi),(="" l="" y="" n="" )="" will="" ~="" ,="" decrease.="" however,="" the="" causes="" of="" the="" decrease="" are="" different,="" in="" the="" former="" case="" s="" will="" decrease,="" and="" in="" the="" latter="" case="" it="" is="" n="" that="" will="" increase.="" whether="" n="" q="" ,="" 9="" n="" ,="" ,="" or="" not="" it="" is="" impossible="" to="" establish="" a="" simple="" general="" law="" that="" will="" apply="" to="" all="" image="" tubes="" because="" of="" variations="" in="" design.="" however,="" neglecting="" v="" ,="" and="" putting="" h="5" mm,="" r="0.2" sec.,="" {(,k?2(x))}1/2="0.015," and="" a="0.1" mm="" as="" reasonable="" values="" into="" eqs.="" (loa)="" and="" (="" l="" l="" a="" )="" ,="" then="" it="" is="" found="" that="" if="" vlqp="">< 6="" x="" lo5=""> RESOLVING POWER O F IMAGE TUBES 559 Q FIQ.4. Output signal-to-noise ratio, ( S / N ) Q oversus resolving parameter a in the case where quantum noise is predominant. mm-2sec-1, the quantum noise is predominant, and if 5,qp % 5 x lo5 electrons mm-2sec- l, the granularity noise is predominant. EXPERIMENTS ON THRESHOLD RESOLUTION According to the above analysis, the optical signal-to-noise ratio is dependent upon the resolving parameter a. To evaluate a, experiments were carried out using an experimental image tube. The modulation transfer function of an experimental image tube, having an effective diameter of 30 mm, and an electro-magnetic focusing lens, was measured. A narrow slit image was projected as the input image, and the line-spread function (1.s.f.) a t the output was recorded by means of a scanning slit and a photomultiplier. Each 1.s.f. could be fitted to a Gaussian curve. One example of an 1.s.f. is shown in Fig. 5. Using this Gaussian approximation, the m.t.f. was calculated analytically by Fourier transformation. The m.t.f. is also given by a Gaussian curve, and the relation between the value of the resolving parameter a and the focusing coil current is given in Fig. 6 . Low Gain Image Tube A single-stage image tube has so low a gain that a considerable photocurrent is needed to observe the output image (in an infra-red image tube, Ylqp M lo8 electrons mm-2sec-1), therefore the granularity noise is predominant. Then setting (SIN) = 3 for threshold detect- 560 9. HASEOAWA FIG.6. Line-spread function. I I x I I - I ‘&II I I I I FIG. 6. Resolving parameter a versus focusing coil current. ability, according to S ~ h a d e ,and ~ {(/32(x))}1’2 = 0.015, Eq. (loa) becomes R(P,)= exp(- a2P12)> 0.018. (12) I n Fig. 7 , the value of a required to fulfil the conditions of Eq. (12) is plotted against F I by a solid line. It is to be noted that if the human eye should have a psychological filtering action against the higher frequency component of the signal, a smaller value should be used for {m))1‘2. 561 RESOLVING POWER OF IMAGE TTJBES An experiment was carried out to verify the result given by Eq. (12)) using the above mentioned image tube. A parallel black-and-white bar pattern was projected on t o the photocathode of the tube, and observation was made with an eyepiece of suitable niagnification to investigate the relation between the value of the threshold resolution and the focusing coil current. The magnitude of the coil current can be