Originally posted by ogl I don't understand how new prism could make OVF 10% brighter...
Good question. There could be two things, I'll start with the one that probably has a bigger effect.
Reason 1.
Through a higher refractive index material, the focusing screen looks closer to the ocular lens. This is not just an optical illusion in that the higher the refractive index, the larger solid angle (
Solid angle - Wikipedia) of light originating from any given point on the focusing screen reaches the ocular lens.
Forget about the prism shape, it's just a hunk of glass with one input surface and one output surface, reflections don't have anything to do with refraction. Instead, let's think about a point on the focusing screen, an empty space, and an ocular lens (Figure A). The point P emits light in a wide angle, and only a fraction of that reaches the lens. In this figure, I used the apex angle of cone of light that reaches the lens instead of the solid angle to represent how wide the cone is.
Next, without changing the distance between the focusing screen and the lens, fill the space with a glass plate with parallel surfaces (Figure B). Because of refraction, the apex angle of cone of light at P that reaches the lens is larger than before. From the lens, the focusing screen appears to be at a new location P', and the apex angle viewed from the lens is the same with the apex angle at P. The larger the refractive index, the larger the apex angle, thus the larger fraction of light from P reaches the lens to be relayed to the eye (thus brighter).
Suppose that you have two glass plates of the exact same thickness, one made of typical glasses like BK7 (n=1.516) and the other made of Ohara S-LAH66 (n=1.7725) that is one of the high refractive index materials mentioned in the patent. How much more solid angle do you gain by using the latter? Let's calculate the ratio of the solid angle!
It turns out that you don't need to know the exact dimensions for the calculations. As far as most of the space is filled with the glass (i.e. distance between the focusing screen and the pentaprism as well as between the pentaprism and the ocular lens are much smaller than the apparent path length of light), and as far as the ocular lens diameter is smaller than the apparent path length of light, the ratio is pretty much the same.
And that ratio is,
- solidAngle(S-LAH66)/solidAngle(BK7) ~ 1.37
(for example if the entire space between the focusing screen and the lens is occupied by the glass, the ratio is ~1.369 when arctan(R/d)~5 degrees, 1.376 if arctan(R/d)~10 degrees).
That is, assuming that the reflection at the input and output surfaces are negligible in both S-LAH66 and BK7 because of good anti-reflection coating, 30-something percent more light reaches the ocular lens originating from P.
Note that this is an
optimistic estimate and should be considered an
upper limit. In reality, though the light is indeed emitted with a large angle from P, the light intensity is not distributed evenly to all directions (e.g. the light is stronger at the center of the cone) and therefore the ratio of the light energy (number of photons) is somewhat smaller than the ratio of the solid angle. There could be other gotchas. 37 percent could easily be 30 or even 20 percent. But this is NOT a few percent effect.
But the view is larger in the new VF, thus increase in the photon number is distributed over a larger area for your view. This will counteract to make your view dimmer. Using the square of the magnification ratio, this effect is
- mag(K-NEW)^2/mag(K-3)^2 = (1.01/0.95)^2 = 1.13.
Ratio of brightness per area on your retina is therefore
- brightness(K-NEW)/brightness(K-3)~ 1.37/1.13 ~ 1.21.
Wow, 20% brighter, maybe this is too much
but as an optimistic estimate that should be considered an upper limit, I claim success.
Reason 2.
The higher the refractive index, the smaller the critical angle (
Total internal reflection - Wikipedia), therefore smaller transmission on roof surfaces for angle of incidence (AOI) smaller than the critical angle. (FYI if AOI is larger than the critical angle, light is 100% reflected without transmission.) This is something that is very briefly mentioned in the patent. There should be such an effect, but it's hard to imagine that this is a huge effect that can possibly explain 10% brighter VF.
The reason why I don't believe this to be the dominant effect is because the AOI on the roof panels is already larger than the critical angle even for BK7 for the vast majority of rays. Critical angle for BK7 and S-LAH66 are 41.3 degrees and 34.3 degrees respectively, while the AOI on roof panels for the light perpendicular to the input surface is 49. 2 degrees.
Originally posted by Kunzite It is explained in the patent. Have you read and understand it? No? Then, you have no choice than to trust the professionals who tells you how it is.
Rather than, say, pretend you know better and they're liars.
Wow, ogl didn't call people liars as far as I see. And no, actually it's not explained in the patent, the patent is not about the brightness of the VF per se.
The patent is about the recipe for multi layer dielectric coating on the roof panels of the roof pentaprism and other prisms with a roof. Without coating, the view quality (contrast and sharpness) suffer, regardless of the refractive index and brightness, according to them. Prior art exists for regular glass materials like BK7, but not for higher refractive index materials, thus this patent.
Sorry for long post!