Motion Picture News (Sept-Oct 1918)

2066 At o t i o 11 Picture Computation of Screen Intensity Mr. R. W. Joyce, Portland, Oregon, writes as follows: " Was much interested in a recent article in your Projection columns, where the light losses in the lens system of a projection machine were figured out. Information of this kind is interesting, and for my part I wish there was more like it published. In the article in the News of August 17 the light lost in the lens system only is stated, but could you not tell us how the amount of light reaching the screen is figured? " In reply: We stopped at the revolving shutter in our previous calculations on projection illumination because we wished to avoid the use of mathematical formulae, which appear to be unpopular with some of our readers. , What was set forth on the previous occasion therefore only represents the efficiency with which the light source of a projector is utilized by the optical system and the 4.80 per cent of the radiation from the source which was represented as getting past the revolving shutter (under very favorable circumstances) represents the transmission coefficient of the projector optical system, or, more strictly stated, of the projector, since the revolving shutter is partly responsible for the reduction of the light. The intensity reaching the screen may be expressed by simple mathematical relationships which, however, involve the transmission coefficients of the various components' of the projector optical system. It will prove useful* therefore, to set forth these coefficients (as previously found) in the form of a convenient reference table. As before, the light source considered is the D. C. arc crater, and for the purpose of compiling the table, its brilliancy is taken as unity. We have, therefore, the following percentage transmissions at various places in the projector optical system, Transmitted by the condenser system — 25.75 per cent of light from source. Transmitted by film picture at aperture — 50 per cent of preceding. Transmitted by objective — 75 per cent of preceding. Transmitted through revolving shutter — 50 per cent of preceding. Now the intensity, I, of the illumination projected upon the screen by an optical lantern (stercopticon or motion picture projector) is given by the expression : _ a" X B X c v~ where a = The diameter of the entrance-pupil of the projection objective or, roughly stated, the diameter of the front component of the objective. B = Brightness per unit area of the source. v — The length of the throw, i.e., the image distance. c = The transmission coefficient of the projection objective and revolving shutter. This is a constant for a given objective and shutter. For the benefit of the more elementary readers a few words may not be amiss regarding the significance of the terms in the above expression, and the values which are assigned to them in working it out. The numerator, a2 X B X c, represents light flux projected to the screen and it is easy to see that the volume of flux so projected must be that part of the light source (required to be at the focus of the objective), of brightness B, which can pass through the opening, or aperture, a2, of the projection objective. But as some of this light is lost in passing through the objective and the revolving shutter, the product of a' X B has further to be multiplied by the transmission co-efficient, c, of the objective and the revolving shutter. This coefficient has a numerical value of about .25 assuming 25 per cent loss in "traversing the objective and 50 per cent cut off by the revolving shutter, as explains detail in our previous article. This product, a2 X B X c has now to be divided by the sq of the length of the throw, represented by v2. The throw image distance, v, must be squared in compliance with the ph metric law of inverse squares. A further point requires explanation and that is the value t assigned to the term B, which represents the brightness per area of the source in our expression. As the expression is based on optical as well as photomi considerations, it will only hold good if the light source is position conjugate to the screen, which means that if the objet is in place and focussed for projecting pictures the value o must be determined at the location of the film picture, i.e., at projection aperture, and must be taken as the brightness tr mitted through the film picture, which then passes to the objec Thus the illuminated film picture at the aperture may be ■ sidered as a secondary light source whose brightness B (i in the above expression) will only be about 12.85 per cent of of the original source (arc crater). The foregoing expression for screen intensity shows how calculated result is arrived at in general, but we will also s how the same may be applied to the determination of the sc brightness in lumens, which as we know, are the modern of illumination measurement. We therefore proceed to de some further terms which will be required. From elemen optical considerations we have : v . ~ . ■=-=M (The magnification of the screen picture). F „ — =A (The effective aperture). a where, as before, v = The length of the throw, or image distance. a = The free aperture of the objective. and F = The equivalent focus of the objective. These derivations are readily apparent when it is recalled the magnification, M, of an optical image is given by the quo of the image-distance (in this case the throw, v) divided by object-distance (in this case the focal length, F, of the objet representing the distance to the film picture or object), \ the effective aperture, A, is the quotient of the diameter of entrance-pupil, a, (the free diameter of front component is . enough for present considerations) into the focal length, F, o objective. Every camera user is acquainted with the signific of these expressions. Proceeding again to the measurement of screen illuminatic modern units which involve the areas of the illuminant and illuminated surface, our expression for the screen intensit will now read: BXc 1 = NT A2 where all the terms have their previously assigned meanings. It is only a few steps now to an expression which will, \ worked out, give a result direct in lumens, for if we put : P = The area of the screen picture and p = " " " " film picture we can write our expression in the form: B X p X c I X P = A" Now, as it has recently been shown (Projection Departr August 24, page 1275) that a lumen may be conceived of as volume of light represented by a cone of unit dimensions w cross-section is in a certain ratio to its height (or length) apparent that I X P in the above equation represents the lun I