The present invention relates to a rear projection screen suited for use in a rear projection type television receiver.
A basic arrangement of an optical system for a rear projection type television receiver or TV is shown in FIG. 1 of the accompanying drawings, in which a reference numeral 1 denotes a projecting cathode ray tube or CRT, 2 denotes a projecting lens, and 3 denotes a projection screen having a diagonal length of about 1 m to 1.5 m onto which an image produced by the CRT is projected.
As is well known, the screen of this type must exhibit a so-called macro-converging action and a micro-diverging action. The term "macro-converging action" refers to an action of the screen that causes rays of light incident on peripheral portions of the screen, spreading divergently from the CRT, to converge toward the central directions, as indicated by broken lines in FIG. 1 whereby an image of a uniform brightness can be seen on the screen over the whole area including the peripheral portion. To attain the macro-converging action, a Fresnel lens is used.
On the other hand, the term "micro-diverging action" means an action when rays of light output from the screen are diverged at a large solid angle so that the image on the screen can be perceived at a uniform brightness even when the image is viewed in a direction inclined relative to the plane of the screen. A lenticular lens is used for attaining the micro-diverging action or function.
Heretofore, there have been proposed various types of screens which can be used as the projection screen 3, a typical one of which is shown in FIG. 2 of the accompanying drawings. In this figure, the reference numeral 4 denotes a lenticular lens surface in which there are formed a number of vertical stripes of such configuration that the rays of light are diverged in the horizontal direction. A numeral 5 denotes a linear Fresnel lens surface constructed with a number of coaxial circular stripes or setbacks each of a sawtooth-like cross-section.
It will be noted that, in the hitherto known screen, the lenticular lens surface and the Fresnel lens surface are formed separately from each other. Accordingly, even a small difference or error in the pitch of the stripe array or even a slight mismatch in the phase relation of the stripe array between both the lens surfaces would give rise to the appearance of interference fringes (moire interference) which degrade the image quality.
In an attempt to reduce the moire interference, it is known to admit particles of glass, silicon oxides or the like into the material (usually, plastic resin such as acryl or the like) of the screen for the purpose of diffusing rays of light in the medium. However, this measure is inevitably accompanied with the side or secondary effect of the degradation of the transmissivity of light which deteriorates the clearness of the projected image.
Next, examination will be made on the efficiency of light transmission of the projection screen. Assuming now that a light of 1 lumen is incident on a unit area of the screen (i.e. assuming that the input intensity of illumination or illuminance is 1 lux), the efficiency of light transmission is represented by T, and luminance of the output light is represented by B(x, y) lumen/m.sup.2 str, where x represents a longitudinal coordinate in radian with y representing a latitudinal coordinate also in radian on the assumption that the output surface of the screen is positioned at the center of a virtual sphere.
The polar coordinate system in concern is illustrated in FIG. 3. In this coordinate system, the following relation for the effeciency of light transmission T applies valid in view of the law of conservation of energy. That is, EQU T=.intg..intg.B(x,y) cos .theta.d.OMEGA. (1)
where .theta. represents a composite angle of x and y, and cos .theta. represents what is referred to as the Lambertian coefficient. According to the spherical geometry, the Lambertian coefficient cos .theta. is given by EQU cos .theta.=cos x.multidot.cos y (2)
Further d.OMEGA. represents a prime element of the solid angle which is given by the following expression (3) in accordance with the spherical geometry. EQU d.OMEGA.=cos ydxdy (3)
With the expressions (2) and (3) taken into account, the expression (1) can be rewritten as follows: ##EQU1##
For simplification of description, it is assumed that B(x, y) is a constant B.sub.O which is independent of x and y in ranges between .+-.X (constant of x and .+-.y (constant) of y, respectively, and the B(x, y) is zero when .vertline.x.vertline.&gt;X and .vertline.y.vertline.&gt;Y, as is shown in FIG. 4. In other words, it is assumed that the screen can be observed at a uniform brightness B.sub.O only in the range where .vertline.x.vertline..ltoreq.X and .vertline.y.vertline..ltoreq.Y.
On the above conditions, the expression (4) can be developed as follows: ##EQU2##
Assuming, by way of example, that the screen exhibits a perfect scattering or diffusion without any loss (i.e. T=1), then X=.pi./2 and Y=.pi./2. Thus, from the expression (5), ##EQU3## This is a well known property of the perfectly scattering surface corresponding to an illuminance of 1 lux and supports the validity of the expression (5).
In this connection, it is important to note that examination or evaluation of a typical screen of the hitherto known structure in the light of the expression (5) has resulted as follows: ##EQU4## In the experiment from which the above data resulted, half-value angles were used as the effective angles of divergence X and Y, as illustrated in FIG. 5.
The efficiency of light transmission T determined on the basis of the above-mentioned data in accordance with the expression (5) is ca. 0.35. In other words, it has surprisingly been found that only about 35% of the light is effectively used, being accompanied with a loss of light which amounts to as great as about 65% in the projection screen of the prior art.
In general, about 4 to 6% of the light is usually lost due to reflection at the interface between the air and the screen made of acryl resin, which means that the total light loss involved at the rear and the front surfaces of the screen is about 10%. Accordingly, a major part of the remaining light loss (about 55%) is ascribable to the side or secondary effect of the agents diffused in the screen material for dealing with the moire interference as described hereinbefore.
As will be appreciated from the foregoing examination, the hitherto known projection screen is very susceptible to the moire interference, which, disadvantageously can not be eliminated without a surprisingly great loss of light.