just a thought
You get a sharper focus when you stop a lens down. That blocks the rays from the outer edges of the lens. So those are the rays with the spherical aberration. The focal point is where the rays that go through the center of the lens focus.
You get a sharper focus when you stop a lens down. That blocks the rays from the outer edges of the lens. So those are the rays with the spherical aberration. The focal point is where the rays that go through the center of the lens focus.
I understand why the f/# effects the image sharpness. What I don’t know is how the FL of the lens is determined on a plain lens with no aperture. Have a look at this pic to see what I mean.
Is the FL determined from the outer rays that converge close to the lens or at one of the points further away? The actual distance in practice would be small but should be measurable with lenses less than f/1.
DJ
Is the FL determined from the outer rays that converge close to the lens or at one of the points further away? The actual distance in practice would be small but should be measurable with lenses less than f/1.
DJ
Attachments
Guy, after thinking about what you said and looking at my last pic some more, I’ve found my answer. I think it is at the point the furthermost away. I came to that conclusion because each incremental step closer to the centre of the lens, the less spherical aberration there is. And it’s not a linear decrease, so the majority of the aberration is confined to the outer edges of the lens. At some infinite point were spherical aberration is no longer a problem, that is the FL.
DJ
DJ
If in-fact the FL is at the further most distance from the lens then it also confirms another theory I have.
When we use a collimating fresnel that has a short FL with a large LCD, the use of a pre-condenser appears to not be needed. Guy, I’ve seen you say this a few times and I believed it to be true as well, until now. With small f/# fresnels the corners will be dimmer this is just physics, the light is going to be less at the corners. But if we place a spherical lens, with its spherical aberration, in between the lamp and fresnel and have the lamp allot closer than the spherical lenses FL, then its aberration will be beneficial in directing more light to the corners. Look at the following pics.
I understand that the use of a pre-condenser isn’t anything new. It's generally thought of for only collecting more light but I think that it has this other benefit as well. If any one can see a hole in my hypotheses, feel free to comment.
DJ
When we use a collimating fresnel that has a short FL with a large LCD, the use of a pre-condenser appears to not be needed. Guy, I’ve seen you say this a few times and I believed it to be true as well, until now. With small f/# fresnels the corners will be dimmer this is just physics, the light is going to be less at the corners. But if we place a spherical lens, with its spherical aberration, in between the lamp and fresnel and have the lamp allot closer than the spherical lenses FL, then its aberration will be beneficial in directing more light to the corners. Look at the following pics.
I understand that the use of a pre-condenser isn’t anything new. It's generally thought of for only collecting more light but I think that it has this other benefit as well. If any one can see a hole in my hypotheses, feel free to comment.
DJ
Know the last one. This is what will happen when the lamp is placed a lot closer to the lens than the FL. All the rays are now diverging with a higher concentration at the outer edge.
This is all theory, I don’t know exactly how much positive effect spherical aberration has, but it seems worthwhile to see if a pre-condenser has the ability to correct dark corners on the 17” projectors we are starting to see.
DJ
This is all theory, I don’t know exactly how much positive effect spherical aberration has, but it seems worthwhile to see if a pre-condenser has the ability to correct dark corners on the 17” projectors we are starting to see.
DJ
Attachments
pre-condensor
The only reason I said pre-condensor lenses don't make much difference in a15" or 17" LCD projector, is because the large 220 mm fl condensor fresnel is already intersecting a pretty big arc of the light. It is difficult to get a pre-condensor lens close enough to the current crop of lamps to capture much more of an arc of the light. If you go to the much smaller form factor lamps, then you could get some use out of a pre-condensor lens.
I think that introducing more spherical aberration in the light path will just give you a bigger lamp arc image at your projection lens. Any part of that that doesn't get into the lens at a useful angle, never makes it to the screen.
I suspect the dim edge problem with 17" LCDs is caused by two things: The spread of the light by the inverse square effect over distance, and the approach to the critical angle near the corners of the fresnel. I think you can solve both problems by decreasing the angle: Use a longer length condensor fresnel, like a 330 mm fl. Of course, then you do need a pre-condensor lens to capture more of the light arc.
The only reason I said pre-condensor lenses don't make much difference in a15" or 17" LCD projector, is because the large 220 mm fl condensor fresnel is already intersecting a pretty big arc of the light. It is difficult to get a pre-condensor lens close enough to the current crop of lamps to capture much more of an arc of the light. If you go to the much smaller form factor lamps, then you could get some use out of a pre-condensor lens.
I think that introducing more spherical aberration in the light path will just give you a bigger lamp arc image at your projection lens. Any part of that that doesn't get into the lens at a useful angle, never makes it to the screen.
I suspect the dim edge problem with 17" LCDs is caused by two things: The spread of the light by the inverse square effect over distance, and the approach to the critical angle near the corners of the fresnel. I think you can solve both problems by decreasing the angle: Use a longer length condensor fresnel, like a 330 mm fl. Of course, then you do need a pre-condensor lens to capture more of the light arc.
For these definition types of questions its best to get a book on optics at your local university. Sorry if that sounds expensive or dull.
We all theorise with the projector stuff because we know there isnt an authorative book on DIY projectors but when we move into areas that have been fully explored by physics and math, there is no point to reinvent the wheel.
Of course doing 2 years undergrad science before moving to business school makes me biased. I always loved the sciences.
We all theorise with the projector stuff because we know there isnt an authorative book on DIY projectors but when we move into areas that have been fully explored by physics and math, there is no point to reinvent the wheel.
Of course doing 2 years undergrad science before moving to business school makes me biased. I always loved the sciences.
The focal length of the lens is measured within the paraxial limit. This means light is near the centeral axis of the lens, and is propagating parallel to this axis. So to answer you question, you look at the light that is coming closest to the center. The spherical abberation is the result of the lens having sperical surfaces, and not parabolas of revolution. If the lens did have these parabola shaped surfaces, then, the light would focus perfectly. Unfortunately its way to expensive to grind precise parabolic lenses, so we settle with spherical.
For people who don't have access to optics books, I have 3 or 4 on my shelf, so feel free to ask away.
For people who don't have access to optics books, I have 3 or 4 on my shelf, so feel free to ask away.
Thanks Moose, That confirms what I suspected. Since you have them books, how much difference is there between where the FL is, to where the rays from the outer edge of the lens focus? Or do you know of a formula to calculate this distance?
DJ
DJ
Not sure on the formula, but I will take a look later. Its going to depend on the size of the lens (both diameter and radius of curvature)
A good starter book, thats fairly comprehensive for its size and price is "Introduction to Modern Optics" by Grant R. Fowles. Its a paperback, so its cheap, heres a link to it on amazon for $11.53 new!
Intro to Modern Optics on Amazon
It was actually used as one of the textbooks for a 4th year level photonics class I took last year. The other textbook is much more comprehensive, but you need a math degree to understand what they are talking about half the time. Its an awesome book though, and if you are more serious about learning this stuff I highly recommend it. Just a warning though, its ten times as thick and ten times the price!
Fundamentals of Photonics
A good starter book, thats fairly comprehensive for its size and price is "Introduction to Modern Optics" by Grant R. Fowles. Its a paperback, so its cheap, heres a link to it on amazon for $11.53 new!
Intro to Modern Optics on Amazon
It was actually used as one of the textbooks for a 4th year level photonics class I took last year. The other textbook is much more comprehensive, but you need a math degree to understand what they are talking about half the time. Its an awesome book though, and if you are more serious about learning this stuff I highly recommend it. Just a warning though, its ten times as thick and ten times the price!
Fundamentals of Photonics
Dazzzla - Equations
Here is the equation you asked for, sorry for the slow response, I've been busy.
The difference between the paraxial focus (the furthest focal point for light in the paraxial limit) and the peripheral focus (light at outer edge of the lens) is given by delta (see attached image)
where:
Delta is the difference between the focii,
r1 is the radius of curvature of the first side of the lens (side closest to parallel light coming in)
r2 is the radius of curvature of the back side of the lens (side closest to focus)
n is refractive index of the lens
h is the height of the ray from the center of the lens, that will strike the peripheral focus
f is focal length of lens
hope this helps
Equation
Here is the equation you asked for, sorry for the slow response, I've been busy.
The difference between the paraxial focus (the furthest focal point for light in the paraxial limit) and the peripheral focus (light at outer edge of the lens) is given by delta (see attached image)
where:
Delta is the difference between the focii,
r1 is the radius of curvature of the first side of the lens (side closest to parallel light coming in)
r2 is the radius of curvature of the back side of the lens (side closest to focus)
n is refractive index of the lens
h is the height of the ray from the center of the lens, that will strike the peripheral focus
f is focal length of lens
hope this helps
Equation
Most of this stuff is already online 😉
http://scienceworld.wolfram.com/physics/topics/OpticalAberrations.html
Trev🙂
http://scienceworld.wolfram.com/physics/topics/OpticalAberrations.html
Trev🙂
- Status
- Not open for further replies.