Sources of Error in and Calibration of the F-Number of Photographic Lenses by Francis E
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U. S. Department of Commerce Research Paper RP1927 National Bureau of Standards Volume 41, October 1948 Part of the Journal of Research of the National Bureau of Standards Sources of Error in and Calibration of the f-Number of Photographic Lenses By Francis E. Washer In problems of photography, where the accuracy of lens marking is critical in determin ing the proper exposure, the various errors to which these markings are subject is of con sid erable in terest. The present report gives the magnitude of such errors that were found to exist in a representative group of 20 le nses having focal lengths that range from 0.5 to 47.5 i,l. In addition, the resul ts of calibration of these lenses by a photometri c method that permits compensation of light losses resulting from absorption, refl ection, and scattering are given. Value of lens transmi ttance for these lenses are shown . A mcthod of p lottin g results of nominal, true, and calibrated I -number is g iven tha t permits quick evaluation of t he magni tude of the over-a ll error in terms of fractions of a stop . I. Introduction McRae [9] and by Gardner [1, 2], who proposed With the advance of photographic technology, several possible methods for calibration of a len . a need has developed for more precise information In the present article, one of the methods described on the light-transmitting characteri tics of photo by Gardner is verifi ed experimentally. The ex graphic objective . In particular, a specific need perimental technique is de cribed, and the varia exists for a more accurate means of marking or tion in performance for 20 lenses, having fo cal calibrating the len es that employ a variable stop lengths that range from 0.5 to 47 .5 in., are shown. for adjusting the len speed. The usual method, Attention is given to som-ces of O1 r01' in the exi t at present, of calibrating a lens is to inscribe a ing marked j -n umber. Lastly, a process is de scale of j -numbers on the diaphragm control. scribed for determining the transmittance of a The ej-number are based upon certain geometric lens from data obtained in the course of calibration. properties of the len , and neglecting errors of marking, provide a satisfactory means of varying II. Apparatus a,nd Method of the speed of the particular lens by definite integral Measurement step.. Unfortunately this system of marking take no cognizance of differences in light-trans The apparatu consi ts essentially of a broad mitting properties that occur among different uniform souree of white light, a sensitive light types of lenses and, in addition, those differences mea uring device, and a holder that can be used that result between lenses of the same type when interchangeably for either mounting the len the surfaces of one have been treated to reduce under test or one of a series of standard diaphragms refl ection 10 ses. each of which has a centrally located circular This problem has been under vigorous attack opening of known diameter. The arrangements for the past 10 years and numerous methods of these clements is the same as that suggested by [1 to 12] 1 have been devised for the rating of lens Gardner [1 ,2] . The relative lens speed is deter speed with re pect to some standard. These mined by a comparison of the quantity of light methods differ in such matters as type of light flux transmitted by a lens with that transmitted source, comparison lens or standard aperture, and by a 'circular opening. By making an appropriate type of light-registering device. The theoretical series of measurements and by proper interpreta a pects of the problem have been discu ed by tion of their significance, the lens can be calibrated in terms of an "ideal" lens having 100-percent 1 Figures in brackets indicate the literature references at the end of tbis pa~er. transmi t tan ce. Calibration of I-Numbers 301 1. Procedure for a Lens minimize error, two sets of data are taken for both A lens in mounted in the holder, and its axis is the lens and the series of standard diaphragms, so alined with the center of the broad uniform source intermingled that random fluctuations in the and the center of the small circular opening in the brightness of the light source and in the sensitivity baffle covering the sensitive element of the light of the light meter can be neglected. measuring device. The front of the lens faces the Ideally, the diameters of the standard dia light source, and the distance separating the rear phragm openings should be so chosen that the nodal point of the lens and the baffle covering the same series of f -numbers are present in both light sensitive element is adjusted to equality, phases of the experiment. Too, the distance, D , with the equivalent focal length, F, of the lens. should equal the equivalent focal length, F; of the Thfl opening in the baffl':) does not usuallv exceed lens. In practice, however, it has proved to be 1 mm, except for some lenses of very l;ng focal more convenient to letD differ fromF and to place length, in which cases it is kept under O.OlF. more reliance upon the ratio, DIA, where A is the All parts of the equipment are shielded so that diameter of the circular opening in a standard only light from the source that passes through the diaphragm. When a wide ' variety of lenses are lens can reach the light-sensitive element. being calibrated, as is the case in this experiment, Readings of the light meter are taken at each of it is simpler to compute the f-number of the stand the marked stop openings. To mllllmlze error ard diaphragm from the ratio, DIA, and to deter arising from back lash, readings are taken both mine the performance of the conventional series for the condition of the setting at the marked off-numbers from the curve of light meter reading f-number being made with the diaphragm ring of versus f -number than to attempt to reproduce the the lens moving in the closing direction and with conventional set of f-numbers by appropriate the diaphragm ring moving in the opening direc selection of values of D and A. tion.2 The readings from these two sets of obser The f-number for a lens is defined by the equa vations are averaged, and this value is taken as the tion 1 accepted reading of the light meter at a given f - number= -2- ' - , (1) marked stop opening. SIn a 2. Procedure for the standard diaphragms where a is the angle between the axis and the ex treme ray of the circular conical bundle transmitted The lens is replaced by one of the series of by the lens. In the case of the standard dia standard diaphragms, which have centrally located phragm, the relation connecting the measured circular openings with known diameters. The quantities D and A is reading of the light meter is taken, and the dis tance D, from the diaphragm to the baffle covering 1 D (2) the light-sensitive element is measured. This A 2 tan a' operation is repeated for several of the standard diaphragms so selected that readings of the light Accordingly, the values of the f -numbers for the meter are obtained throughout the same range of standard diaphragms can readily be computed readings that were observed for the various from the known values of DIA. A sufficiently marked apertures of the lens. The brightness accurate determination of the f -number can be of the source and the sensitivity of the light meter made with the aid of a curve, such as is shown in are kept unchanged throughout both parts of the figure 1. To produce this curve, the values of experiment. To insure constancy of brightness of the quantity, f-number -DIA, are plotted as a the source, a constant voltage transformer is fupction of DIA. Hence, for a given value of used to maintain a constant voltage for the lamps DIA, the increment that must be added thereto tu that illuminate the broad uniform source. To yield the f-number can be easily read from the graph. For values of DIA greater than 15, the , Ten lenses (10, and 12 to 20, incl.) were calibrated in this manner. 'l' he remaining 10 lenses were calibrated witb the diaphragm ring moving in the values of DIA and f -number are equal for all closing direction only in accordance with the recommendation contained in practical purposes, since their difference is less than Report No.6 of the Snbcommittee on Lens Calibration of the Society of Mo tion Picture Engineers on Nov. 6, 1947. 0.1 percent. 302 Journal of Research .14 of Lbe ligh t meter and the j -numbers of an ideal len. Z I n a like manner, the valu es of the scale defl ec .I 0 tion of the li gh t meter are plotted against the j ,C( o number of the acLual lens on the same curve I .0 8 \ sheet. The resulting curve, des ignated curve 2 tt: w CD in fi g ~ll' e 2, is a straigh t line parallel to curve 1, 6 \ ~ .0 Z, but displaced laterally therefrom. This displace LL .04 \ ment shows in a striking manner the effect of li ght losses in the actual lens.