Diffraction Effects and Artifacts in Telescopes like the JWST

[sophiecentaur]

If each photon only interferes with itself

For a 'bright' highly coherent source, there would be many photons involved and, although I really don't like this, you could say that many of the photons will 'interfere with each other'.
I always have a problem with the attempt to interpret wave phenomena in terms of photons; doesn't it call for a real strange concept of the coherence of a single photon? The photon could only actually 'arrive' at one place, which is not a pattern. But the place where it arrives could be at a peak (or null?) in the theoretical pattern and the value will be one.

A stream of single photons will form a pattern, over time. What would determine the spread of the diffraction pattern from the ideal case? Perhaps it would have to be the bandwidth of the original light source, before the 'photon gate' is operated

 

[Devin-M]

I’m amazed by the “volume” of photons it took to produce the pattern— it was a 5 minute exposure so we’re talking about a “beam length” of 55.8 million miles. Considering the aperture diameter was 66 millimeters, that gives a “beam volume” of roughly 29.5 cubic miles of photons to produce the image.

 

[sophiecentaur]

I’m amazed by the “volume” of photons it took to produce the pattern— it was a 5 minute exposure so we’re talking about a “beam length” of 55.8 million miles. Considering the aperture diameter was 66 millimeters, that gives a “beam volume” of roughly 29.5 cubic miles of photons to produce the image.

That tells you how much Energy is in that space but I think that looking at it as a spray of photons is not in the spirit of QM. There is no way that any particular photon is actually inside that cone as photons have no extent not position. Only when a photon interacts with a sensor element can you say when and where the photon existed.

 

[Devin-M]

Only when a photon interacts with a sensor element can you say when and where the photon existed.

Can we say the photons in the middle spike more likely than not went through the set of slits on the left half of the bahtinov mas?

https://en.m.wikipedia.org/wiki/Bahtinov_mask

 

[sophiecentaur]

Can we say the photons in the middle spike more likely than not went through the set of slits on the left half of the bahtinov mas?

I know this is not intuitive but how can you say a photon ‘went through’ / may or may not have taken a path? Remember that Scientists with greater ability than me or (with respect) you struggled with this business. It has been agreed that this approach goes nowhere (nearly a hundred years ago). You need to change the model in your head or you will continue to be confused.

( I can see I have written this in the wrong place. Forgive me. Blame it on the iPhone!

 

[Devin-M]

I know this is not intuitive but how can you say a photon ‘went through’ / may or may not have taken a path? Remember that Scientists with greater ability than me or (with respect) you struggled with this business. It has been agreed that this approach goes nowhere (nearly a hundred years ago). You need to change the model in your head or you will continue to be confused.

I’ll do an experiment and cover the left side of the bahtinov mask with a sheet of black plastic & see if the central spike disappears…

 

[sophiecentaur]

I’ll do an experiment and cover the left side of the bahtinov mask with a sheet of black plastic & see if the central spike disappears…

That would be fun. There are many web pages about the bahtinov mask. You will notice that any good explanations are based on wave theory.

 

[Devin-M]

I’ll compare these 2 options tonight. I predict with the horizontal slits uncovered on the right we will see vertical central spikes, and with the horizontal spikes covered up by masking tape we’ll see no central spike.

I’ll also put a Hydrogen Alpha narrowband filter in front of the image sensor which will only permit photons within 6nm of the 656.2nm wavelength to reach the sensor.

 

[Devin-M]

I did a 5 minute exposure of Polaris at 6400iso through the full Bahtinov Mask (right), and then covered the half of the Bahtinov Mask that had horizontal slits with masking tape and took a second 5 minute exposure (left). Both exposures were at 600mm focal f/9 through a hydrogen alpha narrowband filter. The exposure with the horizontal slits covered was missing its vertical spike:

Aperture during partially covered exposure looked like this:

Uncovered:

Here we have the full frame (uncovered):

 

[Devin-M]

I know this is not intuitive but how can you say a photon ‘went through’ / may or may not have taken a path?

Would or would it not be reasonable to conclude the indicated photons "went through" the indicated slits? Why or why not? Also, to my eye it seems that approximately halving the number of photons to reach the sensor in this manner did nothing to change the length or brightness of the "remaining" diffraction spikes.

 

[Drakkith]

Would or would it not be reasonable to conclude the indicated photons "went through" the indicated slits? Why or why not?

It would not be reasonable to conclude that the photons that ended up in the vertical diffraction spikes went through the right half of the mask. As for why, I admit I don't know the answer well enough to explain it.

Also, to my eye it seems that approximately halving the number of photons to reach the sensor in this manner did nothing to change the length or brightness of the "remaining" diffraction spikes.

The entire image should have approximately half the intensity as before. How that is proportioned into diffraction spikes vs central spot, I don't know, but the eye is a very, very poor sensor for measuring brightness. I recommend looking at the raw image pixel by pixel to get the pixel values to get the ratios. If you want absolute numbers then do the math to convert those values to electrons counted by the sensor during readout and then convert those to incident photons. Keep in mind that the central spot could be so bright it's saturating and you're missing out on photons that should be there when you do your count.

 

[Devin-M]

The entire image should have approximately half the intensity as before. How that is proportioned into diffraction spikes vs central spot, I don't know, but the eye is a very, very poor sensor for measuring brightness. I recommend looking at the raw image pixel by pixel to get the pixel values to get the ratios. If you want absolute numbers then do the math to convert those values to electrons counted by the sensor during readout and then convert those to incident photons. Keep in mind that the central spot could be so bright it's saturating and you're missing out on photons that should be there when you do your count.

I aligned both patterns on top of each other, then isolated a single pixel from the same point on each. Neither had a saturated red channel. One value was 220 out of 256 & the other was 214 out of 256. That's less than a 3% difference in brightness (even though approximately half the lens was covered in one of the exposures).

Here's a link to the RAW files:
https://u.pcloud.link/publink/show?code=kZG4l2VZPdxs8qih835rc40WKQDSfk0xAoSk

 

[Devin-M]

With these 2 horizontal slits I expect vertical spikes only (one pointing up, one pointing down - 2 spikes total):

With these two I expect both vertical and diagonal spikes (one pointing up, one down, and two more diagonal — forming an “x” pattern - 4 spikes total - twice as many spikes, spikes roughly half as bright):

I expect roughly the same total photon count in both cases.

 

[Drakkith]

I aligned both patterns on top of each other, then isolated a single pixel from the same point on each. Neither had a saturated red channel. One value was 220 out of 256 & the other was 214 out of 256. That's less than a 3% difference in brightness (even though approximately half the lens was covered in one of the exposures).

I had a hard time getting a good average value for each 'lobe' in each diffraction spike, so I went with the median, which was much more stable. Additionally, I'm not sure I trust this picture format completely when computing the average. There are many pixels that are exactly zero, suggesting that the camera has altered their values, since between stray light, background light, and thermal noise they should always be above zero. Using the median instead of the average helps filter out this effect, since the value of pixels below or above the median don't affect it in any way, only the number of them, whereas they greatly affect the average value.

Anyways, the median value is about 15-20% higher for each lobe that I measured in the full-aperture picture compared to the half-aperture. This suggests to me that the horizontal gaps in the mask do indeed contribute to the diagonal diffraction spikes.

 

[Devin-M]

I'm not sure I trust this picture format completely when computing the average. There are many pixels that are exactly zero, suggesting that the camera has altered their values, since between stray light, background light, and thermal noise they should always be above zero.

I used photoshop to inspect the RAW files. I discovered even though the RAW files themselves are 14 bit per color channel giving 0-16382 values of red, 0-16382 green, 0-16382 blue, the "color picker" in photoshop is limited to 8 bit (0-255 possible values). Presumably that means if you "pick" a color that is less than (1/256)*16382, it will pick black even if there is color information present ie if the color value is between 0-63 out of 16382 it's converted to 0.

 

[Drakkith]

I used photoshop to inspect the RAW files. I discovered even though the RAW files themselves are 14 bit per color channel giving 0-16382 values of red, 0-16382 green, 0-16382 blue, the "color picker" in photoshop is limited to 8 bit (0-255 possible values). Presumably that means if you "pick" a color that is less than (1/256)*16382, it will pick black even if there is color information present ie if the color value is between 0-63 out of 16382 it's converted to 0.

I don't think that's a problem with Maxim DL (what I used). The picture opens as a greyscale image and I can immediately look at the actual pixel values for all pixels.

 

[Devin-M]

I found the opposite. I copied the same portion of each spike to a separate file, then applied a 3 pixel gaussian blur. When I sampled the same central pixel from each, I found the fully uncovered exposure was dimmer. Fully uncovered had a central red value of 76 of 255 and half covered had a red value of 81 of 255:

 

[Drakkith]

When I sampled the same pixel from each, I found the fully uncovered exposure was dimmer. Fully uncovered had a central red value of 76 of 255 and half covered had a red value of 81 of 255:

Single pixel values are mostly irrelevant, as they are highly subject to noise. Better to use an average, median, or sum of a number of pixels.

 

[Devin-M]

I copied the same portion of each spike to a separate file, then applied a 3 pixel gaussian blur.

The gaussian blur averaged the sampled pixel with the neighboring pixels.

 

[vanhees71]

It would not be reasonable to conclude that the photons that ended up in the vertical diffraction spikes went through the right half of the mask. As for why, I admit I don't know the answer well enough to explain it.

The problem is that people abuse the word "photon" to mean localized (massless) particles to describe "light". That's an idea which goes back to the socalled "old quantum theory" and Einstein's very early ideas on wave-particle duality. This is all outdated for about 100 years. The only correct quantum description of light is quantum electrodynamics, and you are always better off when thinking about light in terms of fields and waves. According to QED a photon is an asymptotic free one-quantum Fock state of the electromagnetic field and as such not localizable in the usual sense, i.e., you cannot even define a position operator in the full meaning of a position observable.

If it comes to the resolution of optical instruments like telescopes it's all about diffraction, i.e., a wave phenomenon, and even if you handle very "dim light", i.e., merely detecting indeed single photons, still the wave nature of light has to be taken into account. Although you'll detect any single photon as one spot (say in a CCD cam), which in some sense is the "particle aspect" of the notion of a photon, the information on the observed object is in collecting sufficiently many photons, and the distribution of the photons is according to the wave picture, i.e., it's given by the energy-density distribution of the electromagnetic field.

The entire image should have approximately half the intensity as before. How that is proportioned into diffraction spikes vs central spot, I don't know, but the eye is a very, very poor sensor for measuring brightness. I recommend looking at the raw image pixel by pixel to get the pixel values to get the ratios. If you want absolute numbers then do the math to convert those values to electrons counted by the sensor during readout and then convert those to incident photons. Keep in mind that the central spot could be so bright it's saturating and you're missing out on photons that should be there when you do your count.

You can calculate all this using classical electrodynamics.

 

[Drakkith]

The gaussian blur averaged the sampled pixel with the neighboring pixels.

Ah, my mistake. I forgot you had averaged them together with a blur.

 

[Devin-M]

I compared the brightness of the center of the 5th diffaction order of the middle spike vs an adjacent spike with the fully uncovered bahtinov mask (same exposure file for both samples). Both samples were copied to separate files and had a 3.0 pixel gaussian blur applied (averaging the values of adjacent pixels to reduce noise), then the central value was sampled. The 5th diffraction order of the middle spike has roughly twice the brightness (144 of 255) of the 5th diffraction order from the adjacent spike (76 of 255). I note that the horizontal slits have roughly twice the collection area compared to each of the other sets of parallel (diagonal) slits...

 

[Devin-M]

Did some more tests with 1, 2 & 4 slits...
RAW Files: https://u.pcloud.link/publink/show?code=kZcjE2VZR1eBfOCgGAYfuGOv9EMgPH3KIR07

 

[Devin-M]

The problem is that people abuse the word "photon" to mean localized (massless) particles to describe "light". That's an idea which goes back to the socalled "old quantum theory" and Einstein's very early ideas on wave-particle duality. This is all outdated for about 100 years. The only correct quantum description of light is quantum electrodynamics, and you are always better off when thinking about light in terms of fields and waves. According to QED a photon is an asymptotic free one-quantum Fock state of the electromagnetic field and as such not localizable in the usual sense, i.e., you cannot even define a position operator in the full meaning of a position observable.

If it comes to the resolution of optical instruments like telescopes it's all about diffraction, i.e., a wave phenomenon, and even if you handle very "dim light", i.e., merely detecting indeed single photons, still the wave nature of light has to be taken into account. Although you'll detect any single photon as one spot (say in a CCD cam), which in some sense is the "particle aspect" of the notion of a photon, the information on the observed object is in collecting sufficiently many photons, and the distribution of the photons is according to the wave picture, i.e., it's given by the energy-density distribution of the electromagnetic field.

1) Here I have only one horizontal slit creating a vertical single slit interference pattern. Is it ok to say the photons forming the pattern "went through" the single slit?

2) Here I have only one diagonal slit creating a diagonal single slit interference pattern. Is it ok to say the photons forming the pattern "went through" the single slit?

3) Here I have both slits open creating what appears to be 2 partially intersecting single slit interference patterns. There are twice as many 2nd and 3rd order diffraction maxima, and some of them don't appear to overlap. Is it ok to say the 2nd & 3rd order diagonal pattern photons in the picture "went through" the diagonal slit and the 2nd & 3rd order vertical pattern photons "went through" the horizontal slit?

4) Here I have 2 horizontal slits open creating an entirely vertical 2 slit interference pattern. Is it ok to say some photons went through one slit, some went through the other, but both patterns entirely overlap so we can't tell which photon went through which slit anymore?

 

[vanhees71]

It's not ok to say the photon went through a specific slit in the two-slit situation. If this were the case, you'd not see the double-slit interference pattern. As I tried to argue above, an electromagnetic wave is a wave and not a localized particle. That's also true for a single-photon state.

 

[Devin-M]

It's not ok to say the photon went through a specific slit in the two-slit situation. If this were the case, you'd not see the double-slit interference pattern.

I stretched out a single pixel vertical strip from the 1) Single Horizontal Slit, 3) Horizontal + Diagonal Slit, & 4) 2 Horizontal Slits. Opening up the diagonal slit in 3) didn't appear to change the position of the dark minima compared to 1) single horizontal slit, but for 4) opening up a 2nd horizontal slit did change the positions of the dark minima (or areas of destructive interference). In other words 3) still looks like a single slit interference pattern compared to 1) from the positions of the dark minima, even though there are 2 slits, but in 4), the positions of the dark minima have changed. Both 3) & 4) have 2 slits.

Single Slit Interference: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html

Double Slit Interference: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html#c2