# B How much space does a single photon occupy?

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1. Jul 17, 2017

### Peter Mason

If a photon leaves a source 4,2 light years away how far apart will it be from a similar photon it was adjacent to (say less than 10^3 wavelengths) when it departed. Does the inverse square law mean that individual photons get further apart and stay the same size or do they occupy a larger space (area). I assume relativity (special or general, I do not really understand) stops photons dispersing in three dimensions. Why? How do the photons line up in space behind each other? If we do not know how do we find out?

I then tried to make a single photon telescope but was deterred by a number of issues.

The stability of the tripod carrying the device. It would need to would maintain its position to better than 2,8 e-17 arcsec, for at lest a few seconds, just to look at the planet 4,2ly away. I suspect that the earth wobbles more than this and certainly the telescope mount. I was aiming to look for an artificial source of protons considerably smaller than the size of the planet.

The smallest pin hole I found was 12,7 μmm that, if mounted at 43º gives a 857 nmm elipse on the detector. Thus the question how big is a photon? Can the photons from the distant source find a way through the pin hole?

As of the time writing the only SPAD device that I have found requires a helium compressor. I go back to the days when if we wanted a photo diode we used a germanium transistor and scraped the paint off. I was planing to buy an avalanche diode from RS.

I could take a broad approach and use the earths inherent gravitational wobble to scan larger parts of the universe with my avalanche diode, with the paint scraped off. A bit of Fourier to filter out the noise and still find the occasional photon streaming from now distant planets and having signatures just a bit different to the background but I need a few thousand of them.

My crude calculation shows the photon density from a 1000 Watt/m^2 source 4,2 light years away is small 1/10^20 m^2.

What does a photon do when it encounters a pin hole of ten wavelengths diameter after it has been isolated by the inverse square law and travelled 4.2 light years? I am encouraged by the thought that should I capture one photon I should see several behind it if I can get the quenching circuit to reset the diode fast enough. How far behind are they?

I am now looking for the slightest encouragement and help to refine the calculations before placing the order with RS.

2. Jul 17, 2017

### phinds

You misunderstand the propagation of electromagnetic waves. During travel there IS no "photon", just a wave. Photons are the result of the wave interacting with another object.

3. Jul 17, 2017

### Staff: Mentor

Photons don't even have a position.

You can look at stars at that distance with your naked eye, without any special alignment requirements.

A pinhole will lower your intensity and give a poor angular resolution. Where is the point?

4. Jul 18, 2017

### Peter Mason

I was trying to isolate a single photon stream emanating from a 1 m^2 source 4,2 ly distant. The idea of the pin hole is to eliminate some of the extraneous clutter.

I now realise from phinds that there is a weak wave front extending over a large area which might be why it can be seen in an optical telescope. The question is how to isolate it the background of other interacting waves?

5. Jul 18, 2017

### Peter Mason

Thank you for the reply. I knew when I wrote that there is a large and fundamental lack of knowledge on my part and was expecting to have a conversation about quantum effects. Your input has however provoked more questions when I consider how a photon arrives in my proposed detector.
As I understand it the wave must start from individual fundamental particles radiating excess energy they have in the form of an electromagnetic wave. Adjacent excited particles from a homogeneous source will have the same frequency but presumably not the same phase relationship. This I further suppose results in a wave that travels, without loss of energy that is another mystery for me, and interacts with other waves it encounters on the way here. This understanding is based principally from observation of sea swell that eventually dissipates allowing me out of harbour. There are often several wave patterns from different directions. Do photons contain directional information? I assume not. Is there a way of gaining directional information possibly using multiple detectors and mathematical combining them, thereby steering the detector more accurately and locking on to one wave source? Again given the sea swell example I am certain that with an array of pressure sensors it would be possible to determine amplitude and direction even if only given the FFT spectrum of each sensor and its position in the array. FFT the photon equivalent .
Does the rate of photon arrival contain information about the temperature of the source or does temperature simply change the wavelength and have no effect on wave amplitude. My assumption is that temperature changes both wavelength and photon rate. My interest is in the frequency and amplitude change of the photon rate.
I found a SPAD 32*32 array Peltier cooled but probably too big and too expensive.

6. Jul 18, 2017

### Staff: Mentor

Unless you place a single-photon source at the source, there is no "single photon stream". And even with such a source, you would only be able to capture a tiny fraction of the emitted photons. With a 1 m2 source there is no way to collimate light well enough, not even if your goal is just to hit Earth.

Forget photons, that just leads to confusion (as seen in this thread). Have a look at waves and diffraction, that is all you need to understand telescopes.

We need telescopes with a diameter of meters to have a chance to see planets as individual spots next to their stars. Otherwise the image of the star is so large that the planet is lost in it.
There is no such thing as a "frequency of excited particles". There are not even excited particles, only excited states of systems. And they do not have an associated frequency.
Only with radio waves or other sufficiently coherent sources where we can measure the phase. Combining them physically is done in interferometers, this can be done with visible light as well (see the Very Large Telescope for example).
Hotter things emit more radiation, but temperature measurements look at the peak frequency, that does not depend on distance (unlike the intensity we receive here).

7. Jul 18, 2017

### sophiecentaur

@Peter Mason
It's a good idea to start with the idea that EM energy travels in the form of waves and that photons are quanta of energy which only exist at the locations where the energy originates from or arrives at and interacts with systems of charge and mass. Any source of EM waves has a finite probability of being detected anywhere in space. Obviously, we can usually accurately predict where we will actually encounter a photon but. if you feel that you need to assign an actual size or extent of a photon then it would have to be infinite - if you have a chance of finding one anywhere - certainly somewhere within the beam you have formed. This is why it's a pointless exercise to try to consider the photon being anywhere until it actually triggers your sensor.
People who first come across the idea of single photon sources seem to think that means that photons can really be treated as little bullets but it would only be in experiments which involve such a sparse production of photons that one could actually identify an individual photon that's transmitted and received. The way the energy gets across the gap is still based on wave theory.

8. Jul 19, 2017

### Peter Mason

But there must be a continuous stream of waves otherwise they would have size and be able to avoid the sensor. Yes we would only capture a tiny fraction of the emitted photons but looking in the time domain they will have a signature.

I will look at waves and diffraction. I was avoiding the maths. Do you have any suggestion where to look?
I cannot control the source. That which I have in mind is an incandescent lamp driven from a 50Hz generator but this is just a prop any abnormal signature would suffice.
I appreciate the impossibility of focusing on such a small target at this range but I am encouraged by sophiecentaur's suggestion that there is a finite probability of finding the wave even here on earth. I was expecting to have to set up a lab on the reverse side of the moon:-). Yesterday evening I was watching waves break along the shore line, albeit on the television, Yes they were well formed having defracted from around the headland but it still seems to me to be a good analogy for the situation here. Is passing the wave through a pinhole1 equivalent to the headland having filtered and polarized it first?

Somehow and admittedly with limited knowledge, the idea of looking further using a small sensor is appealing to me. Rather like probing a surface with an electron microscope. We can obviously capture something from a place known to be in the vicinity of a planet although there is an argument for looking somewhere else as there is a greater probability of something being there (sophiecentaur's infinite search).

Does anyone have access to an optical bench and a single photon detector?
Thank you for the quality of this discussion. I tried this on another science forum but the discussion quickly got lost and was exclusively about the inhabitants of the planet.

It is an aside to the direction I would like this thread take but why is the wave unattenuated and somebody assure me that ALL this wave energy since the beginning of time does not account for dark matter/energy. Stephan Hawkin, the christian bible and probably others, as far as I remember, agree that in the beginning there was only light. (Peter)

1 Diffraction A wave exhibits diffraction when it encounters an obstacle that bends the wave or when it spreads after emerging from an opening. Diffraction effects are more pronounced when the size of the obstacle or opening is comparable to the wavelength of the wave.(Wikipedia)

9. Jul 19, 2017

### sophiecentaur

It depends entirely on your level of Maths. To get anywhere beyond the very basics, you need some idea about Integral Calculus and how the infinitesimal parts of a wave front add together to produce a diffraction pattern.
Probably best to Google "Interference diffraction theory" terms and trawl through until you find something to your liking.

10. Jul 19, 2017

### Staff: Mentor

Optics books.

The challenge in exoplanet imaging is not the brightness of the exoplanets - many of them would be bright enough to be easily visible. The challenge is the nearby star, typically a billion times brighter. You need a very good angular resolution to separate them, and that means you need very large telescopes.
Resolving features on a planet would need telescopes with a size of many kilometers.

The detectors are not an issue, we have highly efficient sensors that capture nearly all the light that comes in.

11. Jul 20, 2017

### Peter Mason

I can do "some idea of" but it would end at solving a differential equation, which I have suggested in the past is something that distinguishes myself from our cat.
I was supposing that I would have a discrete time domain amplitude signal that I could auto correlate to characterise the source and presumably a "simple" FFT might yield something. However you suggest that the diffraction pattern will also be something to consider.

I could probably build or buy the bits to do the the first two by pressing a Raspberrypi into service and involving the local astronomy group (good for my French). The diffraction pattern analysis would be an order of magnitude higher cost and mathematical complexity, involving the array sensor I found in Italy. Although I suppose I could just look at the diffraction pattern or use the Raspberrypi camera to capture it. Looks like I have a project at least for proof of concept.

Can I look from the side?

I agree coming to this I am surprised that single photon detectors exist and I am amazed that so little energy can travel so far and then still be detected. There must come a point where the wave front is so diluted by the inverse square law it is no longer detected.

12. Jul 20, 2017

### sophiecentaur

Sorry butI have no idea what that means in the context of calculating a diffraction pattern or bringing a signal up out of the interfering signal from the star.

13. Jul 20, 2017

### Staff: Mentor

With an 80 square meter telescope (the largest existing telescopes) and a sun-like star as far away as Andromeda (4 million light years), you still get multiple photons per second.
The background noise is important, of course, and you are limited by diffraction.

14. Jul 20, 2017

### sophiecentaur

I have not understood why the OP thinks it's a good thing to be dealing with just one photon at a time when any astronomical observation tries to maximise the number of photons it's using. I think there is a confusion between photons and resolution.

15. Jul 21, 2017

### Peter Mason

Neither do I, that is what I would like to find out.

Ok it may be useful to understand my background. In one sentence I worked as an electronic engineer making microprocessors blink LED's and what you do to make money though I simplify the situation we were quite innovative at the time. The nearest I get to this is measurement of the rate of Gama radiation with a photo-multiplier and a scintillator to measure the thickness of steel plate coming out of a rolling mill. The computer we used occupied a room in the basement and had a drum store of many killo possibly mega bits. Naturally my attempt here is to move things into an area that I can relate to a wiggly line on a cathode ray tube.

If we count the rate of arrival of photons dP/dt or discretely ΔP/Δt it will produce a nice wiggly line. The intention then is to point the contraption at the moon to measure the reflected signature of the only inhabited planet we know, then Mars and Venus for a look at those we suspect have no life. At that point I suspect it all gets cold boring expensive and frustrating gazing into a night sky preferably from the far side of the moon.

I was about to suggest that because light is part of the EM spectrum we would need to developer a new directional sensor similar to a terrestrial TV antenna but at 800 nm. Thinking this is a bit science fiction I searched google and found this. http://piers.org/piersproceedings/d...6aG91fDRBXzEwXzIzMDYucGRmfDE0MDMyMDA0MzEwNA== at the second attempt, the first was a pay site.

This is worrying How many photons per pixel per second and how many photons does the detector miss.

Now back to earth a red telephone box needs paint.

16. Jul 21, 2017

### davenn

all the ones not coming in the front of the detector optics

17. Jul 21, 2017

### Staff: Mentor

Telescopes are doing exactly this. They are a directional sensor for visible light (or infrared, or UV, or whatever the telescope is measuring).
The fraction of light collected by the telescope (relative to the total emission) in my example is 4*10-45. To capture more, you need a larger telescope, or be closer to the star.

18. Jul 21, 2017

### sophiecentaur

This sounds like a fishing expedition in your mum's washing up bowl. You don't know what you're after or bait and hook size. Don't be surprised when you don't get a satisfactory answer for your quest.
You discovered the term
"single photon source" and you want to find a problem to solve with one. There are zillions of websites and forums about astronomy (pro and amateur) and they discuss things like exoplanets on a regular basis. Read around an you will find the relevant factors in this branch of astronomy.
In fact, google the two terms exoplanet and single photon source. See how many hits you get (reputable sources) and that will give you an idea about the worth of the scheme.
. . . . . or take several extra years of measurements.

19. Jul 21, 2017

### Staff: Mentor

That doesn't change the fraction.
It just increases the total light you get.

20. Jul 21, 2017

### sophiecentaur

It increases the signal to noise ratio. SNR imposes the final possible accuracy (discrimination) of all measurements.

21. Jul 21, 2017

### Staff: Mentor

Yes, but it doesn't change the ratio you quoted. A longer measurement time won't capture more than 4*10-45 of the total light the star emits in this time.

22. Jul 21, 2017

### sophiecentaur

Longer measurement time gives a narrower bandwidth. That's Shannon information theory.

23. Jul 21, 2017

### Staff: Mentor

This is completely unrelated to both my initial comment and your follow-up comment.

In visible light in astronomy, observation time is always more than sufficient to have a theoretical spectral resolution way better than the experimental limit. Increasing observation time "only" increases the photon count.

CODEX at the ELT will be one of the best spectrographs ever constructed, with R=135,000. The theoretical time it needs to achieve this? Not even a nanosecond. There is no astronomical observation that lasts only a nanosecond. Moving the telescope alone takes minutes.

24. Jul 21, 2017

### sophiecentaur

That is not a well informed post at all. Detecting a low level signal in the presence of a high level signal is only possible if the noise level is comparable with or lower than the level of the low signal or its effect on the big signal. Snr can be improved in several ways. You are effectively implying that imply that exoplanets should have been detected years ago, if all that counts is the level of light received from the star. We know that they have only been found in the last twenty or so years.
The time to complain that the level of the thread is too low for a lot of the comments was long ago. Size of a Photon can only be dealt with at the lowest level by a curt statement that it is a meaningless concept. Same I brought in Shannon because of your remarks about total number of photons from a star. As with any signal, it isn't the absolute level but the relative amount by which the signal is disturbed by what you are looking for.
I mentioned bandwidth as being relevant but, of course, noise figure and dynamic range are also important.

25. Jul 21, 2017

### Peter Mason

The original post did get a short reply.
My understanding of how light works has been improved and I remain hopeful that a simple single proton detector can yield results. My research as you suggested yields the result that both FFT analysis and correlation techniques are used to analyse interference and diffraction patterns. Further the problem eluded to in my sketch is solved with a star shader. The maths is terrifying and is only resolvable with a clever algorithm that is also beyond me. There are plans to fly such systems in space since the distances needed are large with the 8m telescope they need to observe the planet. I have no idea how to quantify it but a pin hole is likely to be enough to make it achievable here on earth.

If a composite signal and noise are integrated over time the noise will reduce only if it has an mean value tending to zero and is then only useful if the signal of interest has non zero value W.R.T.

Shall I change the title of the thread. I to thought it has exceeded it usefulness. Any suggestion of exoplanet in the title is likely though to attract input about little green men. "Single photon long range camera" perhaps.