The Physics of Digital Cameras

[col]

Colin, you seem to have strangely misunderstood me.


When you say "total number of detected photons" I will assume you mean per pixel. Surely you must see that the number of detected photons per pixel per exposure is proportional to the light intensity at that pixel.

Since it is "photons/second/area" you can increase your photon count by increasing the pixel area or the exposure. However exposure is constrained by other factors so it is out. Since the light intensity at the pixel is dependent on the f-stop and the source intensity you can also increase the photon count by increasing the aperture or by lighting the source, say with flash for example.

Any of these techniques will increase the photon count per pixel and hence decrease the Poisson noise.

Increasing the pixel pitch can be achieved by 1) reducing the number of pixels for a given sensor size, a good move, but you can't go too low else you have insufficient resolution for your final image 2) increasing the sensor size for a given number of pixels, fine except that it makes larger cameras with shallower DoF. Lighting the scene is fine but is not always possible or artistically desirable. Increasing aperture is 1) achieved at the expense of DoF and 2) eventually limited by the Abbe Sine Condition. Such are the limiting factors in minimising Poisson noise.

Hi Warren,

Seems like we are in pretty good agreement then, which is great  

However, increasing absolute aperture (which is what matters re the number of photons dumped on the sensor, and thus shot noise) is not " eventually limited by Abbe Sine Condition", but you would know that already if you had read and agreed with my post# 92.

So, yet again, I ask you to tell me if you agree with everything I said in post#92? As simple yes or no would make my life so much easier in future discussion ....

Cheers, Colin

PS. When I say "total number of detected photons", I actually mean over the entire detector, though for simplicity you can take me to mean per pixel. If you do a proper image noise comparison at equivalent resolution, as for example is done by DXOmark, then a good case can be made that what actually matters is the total number of detected photons for the entire image, independent of the size or number of pixels. However, that is a big and possibly controversial topic that I don't want to get into right now, so by all means take me to mean "total number of detected photons per pixel", especially in your yes/no answer as to whether you agree with everything in post# 92 ....

[Jonathan Wienke]

Yes, as you reduce the focal length you condense the radiant energy of a distant object, but there is a limit to this: the Abbe Sine Condition. When you reach the state where the focal length is half the aperture, then the only way to reduce the focal length further is to reduce the aperture and then, of course, you reduce the afferent flux at the lens so the energy density of the image remains the same. You cannot achieve light amplification through optics alone.

Actually you can, but not in the traditional context of light from a subject passing through a lens and being focused on a plane somewhere outside the lens. Consider the following thought experiment:

Suppose you have a sphere of transparent material having a refractive index of 2.37 and a radius of 2.37cm. One of the corollaries of Snell's Law is that all photons that refract into the sphere will pass through a region in the center of the sphere having a radius equal to (R * I / A), where R is the radius of the sphere, A is the speed of light in the sphere's ambient environment, and I is the speed of light within the sphere. If the sphere is in a vacuum, this can be simplified to (radius of sphere) / (refractive index of sphere). The following diagram illustrates this:

[attachment=19523:HemiLens.png]

The blue lines represent photon paths, some of which refract into the sphere, and some of which bypass the sphere's surface. But as you can see, all of the photons that enter the sphere pass through a region in the center of the sphere that is inversely proportional to the refractive index of the sphere. If we hollow out this 1cm region in the center of the sphere and optically bond an absorptive coating to this newly-created inner surface, all photons that enter the sphere will intersect this inner absorptive surface. Assuming an isotropic distribution of photons intersecting the outer surface of the sphere, the photon flux density at this inner surface will be equal to the square of the refractive index of the sphere (the ratio of the area of the outer surface of the sphere divided by the area of the inner surface of the sphere), minus reflective losses (photons that reflect off the surface of the sphere instead of refracting into the sphere). These losses can be calculated by Fresnel's equations.

For a lens having a refractive index of 2.37, these losses are approximately 29.49% (assuming an isotropic distribution of photons intersecting the outer surface of the sphere). The following diagram shows this visually:

[attachment=19524:ABPower.png]

The red line represents total power isotropically distributed relative to the surface of the sphere. The green line represents the percentage of photons that will refract into the surface of the sphere instead of reflecting off the surface of the sphere, given a refractive index of 2.37. The black line is the product of the red line and the green line. The area below the red line graphically represents the total energy of the photon flux at the sphere's outer surface. The area below the black line represents the portion of the total energy that actually enters the sphere, and the area between the black line and the red line represents energy that reflects off the surface of the sphere.

Thus, if the isotropic photon flux density at the outer surface of the sphere is 100 W/m^2, the photon flux density at the inner surface of the sphere will be:

100 * 2.37^2 * (1 - 0.2949) = 396.02 W/m^2

The astute observer will note that this has some interesting ramifications with regard to thermodynamics and equilibrium.

[WarrenMars]

a good case can be made that what actually matters is the total number of detected photons for the entire image, independent of the size or number of pixels.

I don't agree with this position. Yes, you can make a case, but not, in my opinion, a good one.
I don't know what your case would be, but if I were given the job of submitting the case it would be that: on a given screen view or print, the noisiness of small pixels will be canceled out by the pixel binning required to reduce the resolution to that of larger pixels.

Yes, pixel binning improves the per pixel quality of an image, I'm sure we can all see that, but NOT to the extent of a shot that is taken with pixels of that size in the original. Fuji are one camp that is trying this on with their Exmor sensor, but the real world evidence is fooling no one. Any serious photographer prefers a moderate number of large pixels to a large number of moderate pixels. You can hear the cry for megapixel reduction in every forum and review site in the world.

As someone who has used a 5MP compact and a 10MP compact, there is no doubt that I will take the 5MP job EVERY time, pixel binning or no! Even at 2MP image resolution the shots are obviously superior.

As for your thought experiment Jonathon: I'm not sure what you are trying to achieve. You CAN achieve greater energy density than is permissible by the Abbe Sine Condition simply by moving the image plane to the point where the rays converge, a point that is NOT, as a general rule, at the point where the image is in focus. Even for the sun this point is a VERY small amount closer to the lens than the image. For objects that we normally photograph this point is substantially closer than the image. Yes the energy density is greater at this point but they are not in sharp focus, at least not in focus as the photographer knows it. I believe I made this point at the beginning of all this...    

You can also alter the Abbe Sine Condition by altering the refractive index of the external medium. You can do microscopy within high RI oil for example, allowing a considerable increase in minimum f number, but we don't live in an oil bath, so for the real world photographer such considerations are irrelevant.

[Jonathan Wienke]

As for your thought experiment Jonathon: I'm not sure what you are trying to achieve. You CAN achieve greater energy density than is permissible by the Abbe Sine Condition simply by moving the image plane to the point where the rays converge, a point that is NOT, as a general rule, at the point where the image is in focus.

The primary application I have in mind for this doesn't have involve imaging, although there is at least one instance where this is relevant to imaging--the microlenses over photodetectors. The "real" application involves thermal emission and absorption that occurs naturally in the infrared region. The general idea is to take the photons thermally emitted by a large blackbody surface (surface A, the outer black surface in the diagram above) and use refraction to direct the majority of those photons to a second blackbody surface having a much smaller area (surface B, the inner black surface in the diagram). If the blackbody surfaces are thermally insulated from each other to prevent heat transfer via convection or conduction, then according to Stefan-Boltzmann's Law, the increased photon flux density at surface B (compared to surface A) will cause surface B's temperature to rise above the temperature of surface A until the energy thermally emitted by surface B is equal to the energy being absorbed by surface B.

By heatsinking surface A to the ambient environment and placing a thermocouple between surface A and surface B, it is possible to create a device that absorbs thermal energy from its surroundings and converts the absorbed energy into a small amount of electricity. It's not creating or destroying energy, but it does have the novel ability to re-use existing energy (previously considered to be useless/unusable) an indefinite number of times.

[joofa]

The primary application I have in mind for this doesn't have involve imaging, .....

So what is next Jonathan, a Flux-Capacitor?  

[Jonathan Wienke]

So what is next Jonathan, a Flux-Capacitor?  

No, I was thinking more along the lines of a battery replacement for watches, PDAs, cell phones, pacemakers, etc. that would absorb and convert enough ambient thermal energy to electricity to power the device indefinitely, as long as the device's ambient environment was above a minimum temperature. If you lived/worked in a remote area outside the power grid, having a cell phone or GPS that could operate continuously without conventional recharging would be pretty handy, even if it meant paying a hefty price premium when making the initial purchase. For medical implants, eliminating the need for a plutonium-based nuclear generator (the current state of the art for pacemakers) would mean not having to have radioactive material implanted inside your body, and no periodic operations (with the attendant risk of infection and other complications) to replace batteries. Even if the electrical output was only a fraction of a watt, there are plenty of commercial applications where a hefty price increase could be easily justified by the increase in convenience/usability.

How much extra would you pay for a cell phone that never needed to be plugged in to a charger?

[Daniel Browning]

Yes, pixel binning improves the per pixel quality of an image, I'm sure we can all see that, but NOT to the extent of a shot that is taken with pixels of that size in the original.

That is always incorrect for tonal levels dominated by photon-shot noise (i.e. almost all of them at low ISO). The only time when there is even a possibility of advantage for large pixels is in tonal levels where read noise contributes significantly (e.g. low light). But even then, the preponderance of actual shipping cameras demonstrate that smaller pixels are the same or better. The only tenable position is that they would have been even better at read-noise-dominated tonal levels if the pixel size was larger.

Any serious photographer prefers a moderate number of large pixels to a large number of moderate pixels. You can hear the cry for megapixel reduction in every forum and review site in the world.

Most of those people are making huge mistakes in their image comparison/analysis:

• Unequal spatial frequencies.
• Unequal sensor sizes.
• Unequal processing.
• Unequal standards.
• Unequal technology.
• Unequal raw preconditioning.
• Unequal raw converters.
• Unequal standards.
• Flawed Reasoning.
• Out-of-camera images.

For example, one of the most common positions is this:

• Compacts have smaller pixels than DSLR cameras.
• Compacts have more noise than DSLR cameras.
• Therefore smaller pixels cause more noise.

Obviously, there is a logical error in that: correlation is not causation. As you know, the reality is that it is not the small pixels that cause the noise, but small sensors.

Another common position is that smaller pixels have more noise due to collecting fewer photons. This is plainly not the case, as QE per area is generally higher in smaller pixels, or at worst the same. (This thanks to microlenses.)

[AlexB2010]

The noise level is increased in a situation of low light. At good light in base ISO the level of noise even in small sensors is low. The noise in a image is more pronounced in dark areas, so the picture quality is not constant on al zones. When a camera is working with signal amplification, the signal to noise ratio will influence the output most, the raw number of photons captured is only a small part of the equation, since most noise come from the analog amplified signal before the AD converter. Small sensor allow use of CCD architecture that is more efficient than CMOS. Its obvious that the sensor architecture have a maximum theoretical performance based oh physical characteristics of light and a 1 stop increase in real light conversion performance is a huge increase. Taken apart real sensor performance and cosmetical advertisement, there is little room for improvement. So, the particularities of photon isn't the only constrain in noise level on digital photo.
A question that arise is what the picture quality difference at base ISO?
Best,
Alex

[col]

I wrote:

a good case can be made that what actually matters is the total number of detected photons for the entire image, independent of the size or number of pixels.

I don't agree with this position. I don't know what your case would be, but if I were given the job of submitting the case it would be that: on a given screen view or print, the noisiness of small pixels will be canceled out by the pixel binning required to reduce the resolution to that of larger pixels.

Yes, pixel binning improves the per pixel quality of an image, I'm sure we can all see that, but NOT to the extent of a shot that is taken with pixels of that size in the original.

Hi Warren,

Fortunately my statement is not a matter of opinion, but of simple maths.
We are talking here about image noise caused by photon counting statistics.

Consider two cameras, one with 4MP  and the other 16MP, and each detects the same total number of photons, as per my statement.

To  make any fair or meaningful comparsion of image noise, the resultion of both images must be made equal. In this example, the resolution is made identical by binning groups of 4 pixels on the 16MP camera, in which case the number of photons detected by each pixel in the 4MP camera will be the same as for each bin of 4 pixels on the 16MP camera, and therefore the SNR of the two (equal resolution) images will also be the same. End of story. My statement stands correct.

Cheers,  Colin

[col]

The primary application I have in mind for this doesn't have involve imaging, although there is at least one instance where this is relevant to imaging--the microlenses over photodetectors. The "real" application involves thermal emission and absorption that occurs naturally in the infrared region. The general idea is to take the photons thermally emitted by a large blackbody surface (surface A, the outer black surface in the diagram above) and use refraction to direct the majority of those photons to a second blackbody surface having a much smaller area (surface B, the inner black surface in the diagram). If the blackbody surfaces are thermally insulated from each other to prevent heat transfer via convection or conduction, then according to Stefan-Boltzmann's Law, the increased photon flux density at surface B (compared to surface A) will cause surface B's temperature to rise above the temperature of surface A until the energy thermally emitted by surface B is equal to the energy being absorbed by surface B.

By heatsinking surface A to the ambient environment and placing a thermocouple between surface A and surface B, it is possible to create a device that absorbs thermal energy from its surroundings and converts the absorbed energy into a small amount of electricity. It's not creating or destroying energy, but it does have the novel ability to re-use existing energy (previously considered to be useless/unusable) an indefinite number of times.

Your idea is fascinating, Jonathon.

To better understand your proposal, I would like to ask the following. Consider an enclosed room or box, where all the walls are at held at the same temperature. You can paint the inside surfaces black if you like. Can your proposed electricity-producing-device work inside this room? You may put anything you like in the room, except of course, heat or energy sources.

Colin

[Jonathan Wienke]

Your idea is fascinating, Jonathon.

To better understand your proposal, I would like to ask the following. Consider an enclosed room or box, where all the walls are at held at the same temperature. You can paint the inside surfaces black if you like. Can your proposed electricity-producing-device work inside this room? You may put anything you like in the room, except of course, heat or energy sources.

It will, with the following caveat: The load powered by the device must be in the same isolated environment as the device. If the electrical energy produced by the device is allowed to leave the isolated environment, then the isolated environment's temperature will decrease until the device stops functioning. But if all of the electrical energy output is used within the isolated environment, then the heat energy given off by the electrical load (say an incandescent light bulb), either directly or indirectly, will exactly match the heat being absorbed by my proposed device, and the cycle can repeat an indefinite number of times.

My proposed device cannot create new energy, it can only convert existing heat energy from an unusable to a usable form. I have a PowerPoint presentation that explains how it works in more detail posted here, as well as a PDF version. The presentation covers the underlying math and physics in detail, including a detailed section covering why this isn't a violation of the First or Second Law of Thermodynamics. Some experiments I've conducted that appear to verify the theory are also covered.

I'd be interested in feedback on the presentation, particularly regarding the underlying math and physics principles.

[col]

I wrote:

To better understand your proposal, I would like to ask the following. Consider an enclosed room or box, where all the walls are at held at the same temperature. You can paint the inside surfaces black if you like. Can your proposed electricity-producing-device work inside this room? You may put anything you like in the room, except of course, heat or energy sources.

It will, with the following caveat: The load powered by the device must be in the same isolated environment as the device. If the electrical energy produced by the device is allowed to leave the isolated environment, then the isolated environment's temperature will decrease until the device stops functioning. But if all of the electrical energy output is used within the isolated environment, then the heat energy given off by the electrical load (say an incandescent light bulb), either directly or indirectly, will exactly match the heat being absorbed by my proposed device, and the cycle can repeat an indefinite number of times.

My proposed device cannot create new energy, it can only convert existing heat energy from an unusable to a usable form. I have a PowerPoint presentation that explains how it works in more detail posted here, as well as a PDF version. The presentation covers the underlying math and physics in detail, including a detailed section covering why this isn't a violation of the First or Second Law of Thermodynamics. Some experiments I've conducted that appear to verify the theory are also covered.

I'd be interested in feedback on the presentation, particularly regarding the underlying math and physics principles.

I suspect you did not understand exactly what I said, which is that the walls of the room are held at a the same (constant) temperature. I believe that removes your caveat. According to your claims, electrical energy could therefore leave the room, which would attempt to cool the walls but, as I stated that the wall temperature is held constant, there would be a flow of energy from the outside environment into the walls, to maintain the walls at constant temperature. Thus no violation of the first law.

Did I get that right?

Colin

PS. I have not read your presentation as yet, but I will. Interesting stuff. How many people have you run this idea past?

[Jonathan Wienke]

I suspect you did not understand exactly what I said, which is that the walls of the room are held at a the same (constant) temperature. I believe that removes your caveat. According to your claims, electrical energy could therefore leave the room, which would attempt to cool the walls but, as I stated that the wall temperature is held constant, there would be a flow of energy from the outside environment into the walls, to maintain the walls at constant temperature. Thus no violation of the first law.

Oops. You are correct. As long as energy from outside the room is available to replace the heat energy absorbed by the device inside the room and keep the wall temperature constant, then electrical energy output by the device can be used wherever you like. From a thermodynamic perspective, though, it is important for the device to be able to work indefinitely even in a completely isolated environment containing a finite amount of energy. IMO, this is the key difference between my proposal and everything else energy-related I've looked at--my device can operate indefinitely, even when starting out in a completely isolated isothermal environment (no temperature difference between one point and another), as long as all energy output by the device remains within the isolated environment (or closed system).

How many people have you run this idea past?

Several members of my family so far. Only one real skeptic so far thinks it's impossible, but after two years, he has yet to do a rigorous examination of the math and physics and show me anywhere I've misplaced a decimal point or misapplied an equation. He has an excuse though, he is currently deployed and commanding an air base in Iraq. This is actually the first time I've let the idea out in the cold cruel world...

[WarrenMars]

To make any fair or meaningful comparsion of image noise, the resultion of both images must be made equal. In this example, the resolution is made identical by binning groups of 4 pixels on the 16MP camera, in which case the number of photons detected by each pixel in the 4MP camera will be the same as for each bin of 4 pixels on the 16MP camera, and therefore the SNR of the two (equal resolution) images will also be the same. End of story. My statement stands correct.

Although it sounds fine in theory, in the real world  there are various problems with the pixel binning solution.

The main problem is that there is always some loss at the margins of the pixel. You can talk about micro lenses that can bend the light around the depletion zone, but 1) they ain't gonna bend all the light, 2) there's still gonna be appreciable loss at the micro lens boundaries. In your example above, if the small pixels were square with side length 1, then the large pixel would have a boundary length 8 and the 4 small pixels a total boundary length 16. The margin losses inherent in the pixel binning are then DOUBLE those of the unbinned. Since the width of pixel margins is more or less constant, the smaller the pixels the more significant the margin losses. When you're looking at pixel pitches of 3µm² the area taken up by the cell margins is a significant fraction of the total cell area. It follows that the number of photons detected by the bin is significantly less that those detected at the large pixel. Hence photon noise is greater at the bin.

Due to the relatively low electron counts in the small cells other noise sources such as thermal noise and readout error become more significant, in the above example: 4 times more significant in fact!

Then there is the problem of over-large file sizes that take too long to process, slow up your camera, slow up your computer and take up too much room.

[Jonathan Wienke]

Since the width of pixel margins is more or less constant, the smaller the pixels the more significant the margin losses.

This is where you're going off-base--assuming equal margin width. If you have the ability to shrink the physical size of the other parts of the sensor (microlenses, photodetectors, etc.), then you can generally shrink the margin width as well.

[bjanes]

Fortunately my statement is not a matter of opinion, but of simple maths.
We are talking here about image noise caused by photon counting statistics.

Consider two cameras, one with 4MP  and the other 16MP, and each detects the same total number of photons, as per my statement.

To  make any fair or meaningful comparsion of image noise, the resultion of both images must be made equal. In this example, the resolution is made identical by binning groups of 4 pixels on the 16MP camera, in which case the number of photons detected by each pixel in the 4MP camera will be the same as for each bin of 4 pixels on the 16MP camera, and therefore the SNR of the two (equal resolution) images will also be the same. End of story. My statement stands correct.

Cheers,  Colin

Binning can be done in hardware with CCDs. With 2x2 binning one collects 4 times as many photoelectrons with only one read noise as described here. However, if binning is done is software post capture, there are 4 read noises. Until recently, such hardware binning could only be done with monochrome, but the new Sensor+ technology from Phase One allows hardware binning in color. AFAIK no current CMOS sensors can perform hardware binning. You reduce shot noise, but read noise is not affected.

[PierreVandevenne]

Binning can be done in hardware with CCDs. With 2x2 binning one collects 4 times as many photoelectrons with only one read noise as described here. However, if binning is done is software post capture, there are 4 read noises. Until recently, such hardware binning could only be done with monochrome, but the new Sensor+ technology from Phase One allows hardware binning in color. AFAIK no current CMOS sensors can perform hardware binning. You reduce shot noise, but read noise is not affected.

Clever stuff (http://www.directdigitalimaging.com/pdf/PhaseOneSensorPlus.pdf - http://www.phaseone.com/Digital-Backs/P65/...hnologies.aspx), apparently mixing a classical CCD binning approach with a "virtual" green pixel organization similar to Fuji's SuperCCD (http://en.wikipedia.org/wiki/Super_CCD)... Clever, certainly useful, but I wonder if it can be seen as original enough to actually secure a patent.

BTW, did the Expose+ previous technology get its patent or is there a detailed explanation somewhere? Googling for xpose+ patent -pending -angemeldet doesn't give any meanignful result. At first sight, it doesn't look much different from using a temp scaled dark frame. Maybe there's more to it... If I remember well, it was advertised as "patent pending" for the P20+. Shoud have been granted by now. Does anyone know the patent application number?

Apparently the Kodak KAC serie (at least the KAC-5000) is advertised as a CMOS sensor with hardware binning capability. And in that case, the recent patent can be found. http://www.freepatentsonline.com/EP1900191.html

[col]

Oops. You are correct. As long as energy from outside the room is available to replace the heat energy absorbed by the device inside the room and keep the wall temperature constant, then electrical energy output by the device can be used wherever you like. From a thermodynamic perspective, though, it is important for the device to be able to work indefinitely even in a completely isolated environment containing a finite amount of energy. IMO, this is the key difference between my proposal and everything else energy-related I've looked at--my device can operate indefinitely, even when starting out in a completely isolated isothermal environment (no temperature difference between one point and another), as long as all energy output by the device remains within the isolated environment (or closed system).


Several members of my family so far. Only one real skeptic so far thinks it's impossible, but after two years, he has yet to do a rigorous examination of the math and physics and show me anywhere I've misplaced a decimal point or misapplied an equation. He has an excuse though, he is currently deployed and commanding an air base in Iraq. This is actually the first time I've let the idea out in the cold cruel world...

I'm not easily impressed, but your idea, and the thought you have put into it, impresses me greatly. As yet I have only very briefly skimmed over your detailed description, but see no obvious errors.

As with so many potentially attractive methods of harnessing useful energy, I suspect that your idea may be impractical, though theoretically possible. Have you actually calculated/estimated how large a device would need to be to generate 100mW of  electrical energy? As I see it, if you are able to come up with a commercially viable power source based on your idea, then that is bonus, but the theoretical idea is fascinating regardless.

Colin

 

[PierreVandevenne]

Oops. You are correct. As long as energy from outside the room is available to replace the heat energy absorbed by the device inside the room and keep the wall temperature constant, then electrical energy output by the device can be used wherever you like. From a thermodynamic perspective, though, it is important for the device to be able to work indefinitely even in a completely isolated environment containing a finite amount of energy. IMO, this is the key difference between my proposal and everything else energy-related I've looked at--my device can operate indefinitely, even when starting out in a completely isolated isothermal environment (no temperature difference between one point and another), as long as all energy output by the device remains within the isolated environment (or closed system).

Great that it is not creating energy, it would have been suspicious ;-).

Thermodynamically speaking, how does one prevent the completely isolated environment from reaching some kind of thermal equilibrium? Adding conversion steps makes the analysis more complex, yes, but what keeps the system unstable? Assuming the system is unstable, and there is a perpetual flow in a perfectly isolated environment, how does it fundamentally differ from a perpetual motion machine in a frictionless environment?

And, assuming it works in a non isolated environment, ultimately relying on the energy coming from outside the room to produce electricity, how _efficient_ is it at producing it compared to other energy sucking devices?

At first sight, there is a lot of similarities between your machine and that one

http://www.lhup.edu/~dsimanek/museum/sucker.pdf

I'd like to stress the fact that I am impressed by the thought and the experimental work you put into this: not only did you come up with something that is quite close to a very cool "paradox", but you also avoided the obvious pitfall of creating energy ex-nihilo.


 

[Jonathan Wienke]

I'm not easily impressed, but your idea, and the thought you have put into it, impresses me greatly. As yet I have only very briefly skimmed over your detailed description, but see no obvious errors.

As with so many potentially attractive methods of harnessing useful energy, I suspect that your idea may be impractical, though theoretically possible. Have you actually calculated/estimated how large a device would need to be to generate 100mW of  electrical energy? As I see it, if you are able to come up with a commercially viable power source based on your idea, then that is bonus, but the theoretical idea is fascinating regardless.

I did exactly that in slide 22, and came up with 288 mW/cm^3 of device volume at 300K as a rough estimate of achievable power density using currently available thermocouples and other "off the shelf" components. This could possibly be improved on considerably, perhaps by a factor of 10 or 20, by refining the device design. 288 mW/cm^3 is within the realm of practicality for powering cars and other ground vehicles, but probably too heavy/bulky for aircraft. It's certainly within the practical size/weight range for powering laptops, cellphones, wireless security sensors, etc. And for fixed applications (powering a building, etc) it would be just fine--a refrigerator-sized box outside your house could perform all the necessary heating and cooling you'd need, and supply all the electricity you'd need to run your TV, washer/dryer, lights, etc.