Is there a theoretical limit to aperture?

Knoxis · Feb 26, 2016

Hi,

So I know how when one opens up the aperture, say from F4 to F2.8, you get one more stoop light, which basically means the resultant exposure will be twice as bright if using the same shutter speed and ISO. However, I would like to know if there is a theoretical limit to how much light an aperture can let in. Based off of a video posted on YouTube by Matt Granger, there is technically no theoretical limit to how big aperture can get. You could get an F0.01 lens if the money and resources were available. However, I don't see how one could continuously increase aperture and constantly increase exposure at the same time. One can see light levels change throughout the day, so by technicality there is a finite limit to the amount of light present in a scene. So is there a theoretical limit to how big one can increase the aperture so that no more light can be let in? For example, is it possible for the all the possible receivable light in the scene to ever be let in through a lens, so that opening it one more stope lets in no more light as there is technically no more left to let in? There can't possibly be no limit to the light that can be let in, if there is no light left to let in, right?

What's your thought?

J A C S · Mar 1, 2016

Jeff said:
This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

This looks like a microscopy application, with the rays behind the lens parallel to each other. It is just a trivial observation that you cannot collect more light than half of the light radiating from a point source. It is not related to what we discus here. Think about what is there as the image and the object planes switched.

J A C S · Mar 1, 2016

cpw said:
Detail Man said:

cpw said:

...Now, draw a line parallel ...

Click to expand...

Did you possibly intend to (directly above) write "draw a line perpendicular ..." ?

Click to expand...

Hi Detail Man and Jack,

I meant parallel. So I guess I didn't explain too well, but here is a drawing:

You can see the spherical principal surface, and I've drawn this for the case of theta`=24 deg, NA is then 0.407, and F# = 1.23. I disagree with what Nakamura is writing, (i.e. about F# = f/d as being only an approximation), F# is defined as f/d, it does not lose accuracy as shown above, even for the case on down to F# = 0.5. What is the approximation (and what loses accuracy when we go faster), is the way it's usually drawn. The accurate way above has f on the hypotenuse of that triangle (not the base). You can see as we go on down to this 0.5, the spherical surface grows to its hemisphere shape, and how this spherical surface naturally limits the F#=f/d from going below this 0.5.

I have no idea what you are doing there. Are the horizontal lines light rays? Why aren't they refracted? There is no problem constructing a lens that refracts the rays at the periphery to a point as close as you want to the center of the lens in the image plane. What FL this lens has in another story, and the aberrations would be so strong that there would be no clear focus (so the FL is under question).

Jeff · Mar 1, 2016

J A C S said:
Jeff said:

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Click to expand...

This looks like a microscopy application, with the rays behind the lens parallel to each other. It is just a trivial observation that you cannot collect more light than half of the light radiating from a point source. It is not related to what we discus here. Think about what is there as the image and the object planes switched.

Fair enough, but it does address the thermodynamic question raised above, doesn't it?

J A C S · Mar 1, 2016

Jeff said:
J A C S said:

Jeff said:

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Click to expand...

This looks like a microscopy application, with the rays behind the lens parallel to each other. It is just a trivial observation that you cannot collect more light than half of the light radiating from a point source. It is not related to what we discus here. Think about what is there as the image and the object planes switched.

Click to expand...

Fair enough, but it does address the thermodynamic question raised above, doesn't it?

I did not read that part.

Jeff · Mar 1, 2016

J A C S said:
Jeff said:

J A C S said:

Jeff said:

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Click to expand...

This looks like a microscopy application, with the rays behind the lens parallel to each other. It is just a trivial observation that you cannot collect more light than half of the light radiating from a point source. It is not related to what we discus here. Think about what is there as the image and the object planes switched.

Click to expand...

Fair enough, but it does address the thermodynamic question raised above, doesn't it?

Click to expand...

I did not read that part.

Well, if you didn't read it, then I guess we're talking past each other.

tony field · Mar 1, 2016

Jeff said:
tony field said:

alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

Click to expand...

This is tough going for me (lack of remembered knowledge)

Jeff said:
Others are going to be able to give a better argument. But think about it this way.

Suppose you have a light emitting black body at one temperature. Then, though a system of lenses, you reversibly concentrate the light to a spot of higher temperature. In this was possible, uou would be taking energy from a body at one temperature and transferring it to a body at higher temperature without doing any work. The result would be a decrease in the universe's entropy which is contrary to the second law.

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Powerful stuff!

Agree: pages 94-96 does seem to indicate this (with my limited theory at tap). It is the concept of étendue. I need a lot more study to follow this properly. I think, from memory, that the second law does not necessarily apply in a closed system: local entropy can decrease. IMHO, this is obvious: we are a very low entropy human being in a high entropy universe however as we age our entropy decreases for a while until a certain age and then personal local entropy increases until we are at one with the universe

and... of course we have our low entropy cameras!

However, my speculation infers that we are working in a closed system and can either increase or decrease based on the nature of the system. If the number of Joules of collected mirror energy (over time) is concentrated onto a smaller and smaller area, the total energy in that very tiny point can raise the temperature "as high as we want" - effectively, in the closed system, we can increase the entropy (temperature) as we wish - within engineering limits. This is an energy integration over time - and with the assumption that the target area does not re-radiate to any significant degree.

Of course, this is probably a misguided speculation

--
Charles Darwin: "ignorance more frequently begets confidence than does knowledge."
tony
http://www.tphoto.ca

alanr0 · Mar 2, 2016

tony field said:
alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

A couple of problems here.

The second law of thermodynamics absolutely forbids the transfer of heat from a colder to a hotter body without the input of energy from an external source. Heat pumps such as refrigerators or Peltier devices require an energy input. Conversely, you can extract energy from the transfer of heat from a hotter to a colder body.

The angle subtended by the sun is around 1/2 degree, or 0.01 radian. A mirror array with an effective focal length of 100 m will project an image around 1 m in diameter - which is a pretty big brick. If the individual mirrors don't act like perfect imagers, the "point" will be even larger.

You can achieve the effect described if your solar array produces electricity to drives a large (1 MW ?) carbon dioxide laser, which can then heat a small brick to a temperature in excess of the sun's surface. In the process you will release a lot of low grade heat, raising the net entropy of the universe in compliance with the second law of thermodynamics.

Your scientist might benefit from some refresher courses in optics and thermodynamics.

Cheers.

alanr0 · Mar 2, 2016

tony field said:
Jeff said:

tony field said:

alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

Click to expand...

Click to expand...

This is tough going for me (lack of remembered knowledge)

tony field said:

Others are going to be able to give a better argument. But think about it this way.

Suppose you have a light emitting black body at one temperature. Then, though a system of lenses, you reversibly concentrate the light to a spot of higher temperature. In this was possible, uou would be taking energy from a body at one temperature and transferring it to a body at higher temperature without doing any work. The result would be a decrease in the universe's entropy which is contrary to the second law.

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Powerful stuff!

Click to expand...

Agree: pages 94-96 does seem to indicate this (with my limited theory at tap). It is the concept of étendue. I need a lot more study to follow this properly. I think, from memory, that the second law does not necessarily apply in a closed system: local entropy can decrease. IMHO, this is obvious: we are a very low entropy human being in a high entropy universe however as we age our entropy decreases for a while until a certain age and then personal local entropy increases until we are at one with the universe and... of course we have our low entropy cameras!

However, my speculation infers that we are working in a closed system and can either increase or decrease based on the nature of the system. If the number of Joules of collected mirror energy (over time) is concentrated onto a smaller and smaller area, the total energy in that very tiny point can raise the temperature "as high as we want" - effectively, in the closed system, we can increase the entropy (temperature) as we wish - within engineering limits.

For the system you describe, there are physical limits on the degree of concentration that is possible.

If you increase the temperature difference while keeping the total energy constant, entropy decreases - which is not allowed in a closed system. You can raise the temperature in a small local area by pumping heat around, but this will always result in a net increase in entropy within a closed system.

tony field said:
This is an energy integration over time - and with the assumption that the target area does not re-radiate to any significant degree.

But it will re-radiate. Check out Kirchoff's law of thermal radiation.

--
Alan Robinson

alanr0 · Mar 2, 2016

J A C S said:
cpw said:

Detail Man said:

cpw said:

...Now, draw a line parallel ...

Click to expand...

Did you possibly intend to (directly above) write "draw a line perpendicular ..." ?

Click to expand...

Hi Detail Man and Jack,

I meant parallel. So I guess I didn't explain too well, but here is a drawing:

You can see the spherical principal surface, and I've drawn this for the case of theta`=24 deg, NA is then 0.407, and F# = 1.23. I disagree with what Nakamura is writing, (i.e. about F# = f/d as being only an approximation), F# is defined as f/d, it does not lose accuracy as shown above, even for the case on down to F# = 0.5. What is the approximation (and what loses accuracy when we go faster), is the way it's usually drawn. The accurate way above has f on the hypotenuse of that triangle (not the base). You can see as we go on down to this 0.5, the spherical surface grows to its hemisphere shape, and how this spherical surface naturally limits the F#=f/d from going below this 0.5.

Click to expand...

I have no idea what you are doing there. Are the horizontal lines light rays? Why aren't they refracted? There is no problem constructing a lens that refracts the rays at the periphery to a point as close as you want to the center of the lens in the image plane. What FL this lens has in another story, and the aberrations would be so strong that there would be no clear focus (so the FL is under question).

Chris is using the concept of principal surface - which says that the lens acts as if all the refraction occurs at the principal surface. In the diagram above the rays act as if they follow the dotted blue lines, but the actual path through a single element thick lens would be a straight line from the intersection with the front surface to the intersection with the rear surface. The concept becomes most useful for more complex lenses with multiple refracting surfaces.

I have not read Nakamura. I agree that (F# = f/d) is exact for an ideal lens with a spherical principal surface centred on the focal point. It will be an approximation for lenses which are not ideal. This will apply to most lenses designed for a flat field over a finite field of view.

--
Alan Robinson

Jack Hogan · Mar 2, 2016

cpw said:
I disagree with what Nakamura is writing, (i.e. about F# = f/d as being only an approximation), F# is defined as f/d, it does not lose accuracy as shown above, even for the case on down to F# = 0.5. What is the approximation (and what loses accuracy when we go faster), is the way it's usually drawn. The accurate way above has f on the hypotenuse of that triangle (not the base). You can see as we go on down to this 0.5, the spherical surface grows to its hemisphere shape, and how this spherical surface naturally limits the F#=f/d from going below this 0.5.

Nice diagram Chris, you make a valid point in this specific case with focal length f defined as in it.

However f is defined in many other ways in practice and this creates confusion. I agree with Nakamura that defining f/# as f/d is imprecise in most cases and leads to many incorrect conclusions and wikipedia pages, some of which discussed in this thread. There is no such misinterpretation problem on the other hand when defining f-number by the opening angle theta'.

Jack

Jeff · Mar 2, 2016

alanr0 said:
tony field said:

Jeff said:

tony field said:

alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

Click to expand...

Click to expand...

This is tough going for me (lack of remembered knowledge)

alanr0 said:

Others are going to be able to give a better argument. But think about it this way.

Suppose you have a light emitting black body at one temperature. Then, though a system of lenses, you reversibly concentrate the light to a spot of higher temperature. In this was possible, uou would be taking energy from a body at one temperature and transferring it to a body at higher temperature without doing any work. The result would be a decrease in the universe's entropy which is contrary to the second law.

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Powerful stuff!

Click to expand...

Agree: pages 94-96 does seem to indicate this (with my limited theory at tap). It is the concept of étendue. I need a lot more study to follow this properly. I think, from memory, that the second law does not necessarily apply in a closed system: local entropy can decrease. IMHO, this is obvious: we are a very low entropy human being in a high entropy universe however as we age our entropy decreases for a while until a certain age and then personal local entropy increases until we are at one with the universe and... of course we have our low entropy cameras!

However, my speculation infers that we are working in a closed system and can either increase or decrease based on the nature of the system. If the number of Joules of collected mirror energy (over time) is concentrated onto a smaller and smaller area, the total energy in that very tiny point can raise the temperature "as high as we want" - effectively, in the closed system, we can increase the entropy (temperature) as we wish - within engineering limits.

Click to expand...

For the system you describe, there are physical limits on the degree of concentration that is possible.

If you increase the temperature difference while keeping the total energy constant, entropy decreases - which is not allowed in a closed system. You can raise the temperature in a small local area by pumping heat around, but this will always result in a net increase in entropy within a closed system.

alanr0 said:

This is an energy integration over time - and with the assumption that the target area does not re-radiate to any significant degree.

Click to expand...

But it will re-radiate. Check out Kirchoff's law of thermal radiation.

tony field · Mar 2, 2016

Jeff said:
alanr0 said:

tony field said:

Jeff said:

tony field said:

alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

Click to expand...

Click to expand...

This is tough going for me (lack of remembered knowledge)

Jeff said:

Others are going to be able to give a better argument. But think about it this way.

Suppose you have a light emitting black body at one temperature. Then, though a system of lenses, you reversibly concentrate the light to a spot of higher temperature. In this was possible, uou would be taking energy from a body at one temperature and transferring it to a body at higher temperature without doing any work. The result would be a decrease in the universe's entropy which is contrary to the second law.

This is a fascinating discussion, which prompted me to look at a few references on conservation of etendue and the relationship to thermodynamics. One of the earliest seems to be the a paper by Ari Rabi (http://www.physics.arizona.edu/~cronin/Solar/References/Solar Concentrator Models/V Trough/RAB76.pdf). An interesting point in the paper is that the second law establishes a lower bound on f-number, namely f >= 1/2. (See page 96 of the paper).

Powerful stuff!

Click to expand...

Agree: pages 94-96 does seem to indicate this (with my limited theory at tap). It is the concept of étendue. I need a lot more study to follow this properly. I think, from memory, that the second law does not necessarily apply in a closed system: local entropy can decrease. IMHO, this is obvious: we are a very low entropy human being in a high entropy universe however as we age our entropy decreases for a while until a certain age and then personal local entropy increases until we are at one with the universe and... of course we have our low entropy cameras!

However, my speculation infers that we are working in a closed system and can either increase or decrease based on the nature of the system. If the number of Joules of collected mirror energy (over time) is concentrated onto a smaller and smaller area, the total energy in that very tiny point can raise the temperature "as high as we want" - effectively, in the closed system, we can increase the entropy (temperature) as we wish - within engineering limits.

Click to expand...

For the system you describe, there are physical limits on the degree of concentration that is possible.

If you increase the temperature difference while keeping the total energy constant, entropy decreases - which is not allowed in a closed system. You can raise the temperature in a small local area by pumping heat around, but this will always result in a net increase in entropy within a closed system.

Jeff said:

This is an energy integration over time - and with the assumption that the target area does not re-radiate to any significant degree.

Click to expand...

But it will re-radiate. Check out Kirchoff's law of thermal radiation.

Click to expand...

tony field · Mar 2, 2016

alanr0 said:
tony field said:

alanr0 said:

tony field said:

Joe Pineapples II said:

tony field said:

A note on this subject a long while ago (if memory serves me) by Bob indicated that the issue is with the index of refraction of modern glass. He intimated that new novel materials might overcome the problem.

Click to expand...

I believe the 0.5 limit is a hard limit set by the fact that sin(x) is never great than 1 (for real x). Approaching the limit in a real lens may well be a question of the available high refractive index glass. I guess diffractive optics can approach the limit closer but at the cost of other problems.

Joe

Click to expand...

This is my impression as well. However, maybe there are image forming technologies that we have not yet considered as viable. For example, simple non-image forming technology can focus the sunlight into a "single small area" where the "small area" temperature is greater than the surface temperature of the sun.

Click to expand...

Do you have a reference? This seems incompatible with the second law of thermodynamics. :-(

Click to expand...

No direct reference. I was watching a science documentary about "light". One of the expositions was about a light-concentrating facility in the USA in which a very large number of adjustable mirrors (think of a couple of football field or more in terms of surface area) could be accurately focused onto a point the size of a brick or smaller. The scientist stated that, at the point of focus, the temperature could be hotter than the surface of the sun.

Makes to me ... and does not break the second law (in any way that I can see)

Click to expand...

A couple of problems here.

The second law of thermodynamics absolutely forbids the transfer of heat from a colder to a hotter body without the input of energy from an external source. Heat pumps such as refrigerators or Peltier devices require an energy input. Conversely, you can extract energy from the transfer of heat from a hotter to a colder body.

The angle subtended by the sun is around 1/2 degree, or 0.01 radian. A mirror array with an effective focal length of 100 m will project an image around 1 m in diameter - which is a pretty big brick. If the individual mirrors don't act like perfect imagers, the "point" will be even larger.

You can achieve the effect described if your solar array produces electricity to drives a large (1 MW ?) carbon dioxide laser, which can then heat a small brick to a temperature in excess of the sun's surface. In the process you will release a lot of low grade heat, raising the net entropy of the universe in compliance with the second law of thermodynamics.

Your scientist might benefit from some refresher courses in optics and thermodynamics.

Cheers.

nikanth · Mar 2, 2016

1. Is it possible to create a 400mm f/2.8 lens? Yes

2. Is it possible to create Brenizer method bokeh rama using the 400mm f/2.8 lens to create an image with FOV equivalent of 20mm? And won't it be equivalent to 20mm @ f/0.14 ?

3. Is it possible to create a speedbooster for a 20x crop sensor? If yes won't the 400 mm f/2.8 essentially become a 20mm f/0.14 on that 20x crop camera?

If not possible, why?

cpw · Mar 2, 2016

Yep, thanks Alan, nicely stated.

Chris

J A C S · Mar 2, 2016

alanr0 said:
J A C S said:

cpw said:

Detail Man said:

cpw said:

...Now, draw a line parallel ...

Click to expand...

Did you possibly intend to (directly above) write "draw a line perpendicular ..." ?

Click to expand...

Hi Detail Man and Jack,

I meant parallel. So I guess I didn't explain too well, but here is a drawing:

You can see the spherical principal surface, and I've drawn this for the case of theta`=24 deg, NA is then 0.407, and F# = 1.23. I disagree with what Nakamura is writing, (i.e. about F# = f/d as being only an approximation), F# is defined as f/d, it does not lose accuracy as shown above, even for the case on down to F# = 0.5. What is the approximation (and what loses accuracy when we go faster), is the way it's usually drawn. The accurate way above has f on the hypotenuse of that triangle (not the base). You can see as we go on down to this 0.5, the spherical surface grows to its hemisphere shape, and how this spherical surface naturally limits the F#=f/d from going below this 0.5.

Click to expand...

I have no idea what you are doing there. Are the horizontal lines light rays? Why aren't they refracted? There is no problem constructing a lens that refracts the rays at the periphery to a point as close as you want to the center of the lens in the image plane. What FL this lens has in another story, and the aberrations would be so strong that there would be no clear focus (so the FL is under question).

Click to expand...

Chris is using the concept of principal surface - which says that the lens acts as if all the refraction occurs at the principal surface. In the diagram above the rays act as if they follow the dotted blue lines, but the actual path through a single element thick lens would be a straight line from the intersection with the front surface to the intersection with the rear surface. The concept becomes most useful for more complex lenses with multiple refracting surfaces.

OK, I see. Why should be the principal surface be a sphere then? An extreme fast lens would have a surface that would not be a sphere or hyperbolic, or parabolic, and who knows what the principal surface might look like. Here is a simulation with rays at the periphery "fast" enough but the rays close to the center are not. OpticalRayTracer does not allow me to change the shape of the lens much. You need an extreme shape of the front surface to reduce the aberrations, and who knows what you need to do with the back surface and how that would limit the FL. And then this lens may be focusing satisfactory in the center only.

So I do not see this as a simple question. A lot of formulas in optics are based on certain assumptions and approximations that you need to violate to create a super fast lens with glass. The choice of the shape of the surfaces is a non-trivial non-linear optimization problem, and adding more elements to the lens will only make it harder.

Jack Hogan · Mar 2, 2016

nikanth said:
1. Is it possible to create a 400mm f/2.8 lens? Yes

2. ...

OT

nikanth said:
3. Is it possible to create a speedbooster for a 20x crop sensor? If yes won't the 400 mm f/2.8 essentially become a 20mm f/0.14 on that 20x crop camera?

From what I understand a speedbooster is just an additional element that is added externally to a lens to reduce its focal length by a small factor, say 0.7. As long as the amount of reduction is small and the lens can physically accommodate the new focal length that's ok*, you now have a long focal length lens adapted to have a shorter focal length. Mind you, it most certainly would have been better to buy a lens designed for the shorter focal length in the first place.

nikanth said:
If not possible, why?

If the speedbooster reduced the focal length a lot more than that small amount the lens would no longer work as designed because it would run into its physical limits. If one wanted such a smaller focal length one would have to buy a lens designed for it, with its own physical limits. You could definitely have a 20mm lens as big as a 400mm lens. But everything discussed earlier about f-number and equivalence for practical photography lenses would still apply, and N would in that case be greater than 0.5.

Jack

* I haven't done the math, but I am pretty sure that N will reduce less than linearly with focal length in this case.

alanr0 · Mar 2, 2016

J A C S said:
alanr0 said:

J A C S said:

cpw said:

Detail Man said:

cpw said:

...Now, draw a line parallel ...

Click to expand...

Did you possibly intend to (directly above) write "draw a line perpendicular ..." ?

Click to expand...

Hi Detail Man and Jack,

I meant parallel. So I guess I didn't explain too well, but here is a drawing:

You can see the spherical principal surface, and I've drawn this for the case of theta`=24 deg, NA is then 0.407, and F# = 1.23. I disagree with what Nakamura is writing, (i.e. about F# = f/d as being only an approximation), F# is defined as f/d, it does not lose accuracy as shown above, even for the case on down to F# = 0.5. What is the approximation (and what loses accuracy when we go faster), is the way it's usually drawn. The accurate way above has f on the hypotenuse of that triangle (not the base). You can see as we go on down to this 0.5, the spherical surface grows to its hemisphere shape, and how this spherical surface naturally limits the F#=f/d from going below this 0.5.

Click to expand...

I have no idea what you are doing there. Are the horizontal lines light rays? Why aren't they refracted? There is no problem constructing a lens that refracts the rays at the periphery to a point as close as you want to the center of the lens in the image plane. What FL this lens has in another story, and the aberrations would be so strong that there would be no clear focus (so the FL is under question).

Click to expand...

Chris is using the concept of principal surface - which says that the lens acts as if all the refraction occurs at the principal surface. In the diagram above the rays act as if they follow the dotted blue lines, but the actual path through a single element thick lens would be a straight line from the intersection with the front surface to the intersection with the rear surface. The concept becomes most useful for more complex lenses with multiple refracting surfaces.

Click to expand...

OK, I see. Why should be the principal surface be a sphere then? An extreme fast lens would have a surface that would not be a sphere or hyperbolic, or parabolic, and who knows what the principal surface might look like. Here is a simulation with rays at the periphery "fast" enough but the rays close to the center are not. OpticalRayTracer does not allow me to change the shape of the lens much. You need an extreme shape of the front surface to reduce the aberrations, and who knows what you need to do with the back surface and how that would limit the FL. And then this lens may be focusing satisfactory in the center only.

So I do not see this as a simple question. A lot of formulas in optics are based on certain assumptions and approximations that you need to violate to create a super fast lens with glass. The choice of the shape of the surfaces is a non-trivial non-linear optimization problem, and adding more elements to the lens will only make it harder.

You should get closer to a decently corrected lens in OptcalRayTracer with a hyperboloid front surface. It won't be perfect, but for fixed lens thickness, you only have a 1-dimensional optimisation of cf to minimise spherical aberration.

If you can handle more complex surfaces, check out the data provided with commercial aspheric lenses, such as those offered by Thorlabs, e.g. ACL25416U 16 mm focal length NA 0.79. This won't have a wide field of view, but should be decently corrected on-axis.

A spherical principal surface is required to meet the Abbe sine condition for a distant object. It also ensures that etendue is conserved on-axis.

--
Alan Robinson

J A C S · Mar 2, 2016

Jack Hogan said:
nikanth said:

1. Is it possible to create a 400mm f/2.8 lens? Yes

2. ...

Click to expand...

OT

Jack Hogan said:

3. Is it possible to create a speedbooster for a 20x crop sensor? If yes won't the 400 mm f/2.8 essentially become a 20mm f/0.14 on that 20x crop camera?

Click to expand...

From what I understand a speedbooster is just an additional element that is added externally to a lens to reduce its focal length by a small factor, say 0.7. As long as the amount of reduction is small and the lens can physically accommodate the new focal length that's ok*, you now have a long focal length lens adapted to have a shorter focal length. Mind you, it most certainly would have been better to buy a lens designed for the shorter focal length in the first place.

Jack Hogan said:

If not possible, why?

Click to expand...

If the speedbooster reduced the focal length a lot more than that small amount the lens would no longer work as designed because it would run into its physical limits. If one wanted such a smaller focal length one would have to buy a lens designed for it, with its own physical limits. You could definitely have a 20mm lens as big as a 400mm lens. But everything discussed earlier about f-number and equivalence for practical photography lenses would still apply, and N would in that case be greater than 0.5.

The way I see it, a 400/2.8 with a 10x booster is, as you say, a non-optimally designed 40/0.28 lens. But if we believe that a 40/0.28 cannot exist, then a non-optimal one would not exist, either.

In other words, such a booster would be an extremely fast lens as well, and we are back to square one.

J A C S · Mar 2, 2016

alanr0 said:
A spherical principal surface is required to meet the Abbe sine condition for a distant object.

Why? I am sure that it will help but why is it required? And what is the penalty if it is not?

alanr0 said:
It also ensures that etendue is conserved on-axis.

That was an interesting link. I always wondered how Liouville's theorem is used in optics. Well, unless you have diffusion, etc., the etendue is always conserved.

P.S. I just derived it myself, it does not be a sphere if you want the Abe condition to be satisfied.

Is there a theoretical limit to aperture?

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