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Effect of eyepiece when digiscoping

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#1 LeeNixon

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Posted 17 July 2024 - 05:27 AM

I understand the 500 rule used to calculate the longest exposure that will avoid obvious star trailing. However, when digiscoping, there is an eyepiece on the scope, plus the lens of the camera (in this case a phone camera). the magnification of a given eyepiece will affect that rule as a higher magnification will speed up the movement of stars through the field of view in addition to whatever focal length is on my camera lens (smart phone). What I'm wondering is whether there is a way of calculating for the phone and eyepiece, or is it just trial and error because of the different factors involved?

Edited by LeeNixon, 17 July 2024 - 05:44 AM.

#2 ButterFly

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Posted 17 July 2024 - 06:10 AM

The 500 rule comes from the days of photographic emulsion.  It has a pixel scale built into it based on chemistry, and it is fixed.  These days, pixels come in many sizes, and don't depend on chemistry.  You know how big your pixels actually are, so use that information.

To find the trailing you can tolerate, start with what a trail means: the star moved over by at least one pixel.  Then, it becomes rather simple.  Simply find how long it takes for a star to move by one pixel.  If you really, really don't like any oblong to your stars, make it half a pixel.

First, you are digiscoping, so everything behind the eyepiece creates its own pixel scale at the sensor.  That depends on your objective focal length, and your pixel size, calculated as though there were nothing in front of the objective other than sky.  Calculate how long it would take a star to move by one pixel with just the objective and the sensor.  Then, because you are looking through an eyepiece, the star speed simply gets magnified by the amount of magnification.  So, the time drops by a factor of the magnification.

Note that the time it takes a star to move by one pixel depends on the declination of the target.  The celestial poles don't move at all, whereas everything moves the fastest at the celestial equator.  To adjust for that, calculate the times at the celestial equator with 15.042 arcseconds per second of motion.  Then, divide by cos(Dec).  For the special case where field of view includes the celestial pole, everything will spin around that.  So for that case, use the lowest Dec the field of view includes.  The effect is the same as though the native pixel scale were divided by your magnification.

As an example, lets say your objective and your pixel size make a pixel scale of one arcsecond per pixel.  You would get one pixels worth of star motion at the celestial equator in 1 [arcsecond per pixel] / 15.042 [arcseconds per second], or about 66.5 ms.  Now, put that same setup behind an eyepiece that magnifies 10x.  You would get one pixels worth of star motion at the celestial equator in 1 [arcsecond per pixel] / ( 10 x 15.042 [arcseconds per second]), or about 6.65 ms.  If the target is at a Dec of 45 degrees, divide by cos (45) ~ 0.707, so it comes out to 6.65ms / 0.707 ~ 9.4 ms.  It's the same result as with a pixel scale of the whole system of 0.1 arcseconds per pixel!

With a phone, you may not know either of your pixel size, or your phone objective's focal length.  In that case, it's a lot easier to just work with the actual pixel scale of the whole system, as seen at the sensor.  Take an image with a bunch of stars in it, then plate solve that image using astrometry.net.  Other solvers will probably fail due to quality, or complete lack of knowledge of the pixel scale.  Astrometry.net can solve just about anything.  Once you have the pixel scale of your whole system (telescope plus eyepiece plus objective plus sensor), just work with the ordinary 15.042 arcseconds per second of motion and proceed from there.

Edited by ButterFly, 17 July 2024 - 07:13 AM.

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#3 Astrojensen

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Posted 17 July 2024 - 06:16 AM

To calculate the focal length of the complete system when doing afocal imaging ("digiscoping"), just take the magnification of the eyepiece you're imaging through, and multiply it with the camera focal length.

Example: I use a 40mm eyepiece on a 2250mm focal length Maksutov. This gives 56x. The focal length of my camera lens in my phone is 5.24mm, according to manufacturer's specifications. The focal length is then 56 x 5.24 = 293.44mm

Clear skies!

Thomas, Denmark

Post was edited, because ButterFly explained things better than I did.

Edited by Astrojensen, 17 July 2024 - 06:19 AM.

#4 deSitter

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Posted 17 July 2024 - 09:27 AM

This is called afocal photography - telescope and camera focused at infinity. The camera acts just as your eye does in making the final image.

It also acts just as your eye does in terms of the exit pupil of the telescope - namely if the entrance pupil of the camera is smaller than the exit pupil of the scope, you will effectively be stopping down the telescope - and if the camera is not right at the exit pupil, you'll get vignetting or blackouts. (A third complication is that the camera must be square to the optical axis, else you'll get spurious colors.)

A typical phone camera aperture is about 3mm I seem to remember. So your telescope will need to make a exit pupil of 3mm or less to use the complete telescope aperture. Meaning, medium to high power.

But the most difficult problem is the placement of the exit pupil of the eyepiece. You need a long eye relief eyepiece, and that means low power usually, meaning too large an exit pupil. You also need one with little "spherical aberration of the exit pupil", which rules out almost all wide field eyepieces. (Orthoscopics work best for me.)

The best eyepieces are thus those that combine sufficient exit pupil and eye relief. Most eyepieces don't work well. Using a regular camera with a much larger aperture eliminates the too-large exit pupil issue.

The upshot of all this is that, although it is the easiest form of photography through a telescope in principle, in practice it is hard to satisfy the constraints with most eyepieces and a cell phone camera. I have had good results with a pocket camera whose focus can be fixed at infinity, but never with a phone. Colored fringes are hard to avoid. The camera sees things you learn to not see visually.

-drl

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#5 Astrojensen

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Posted 17 July 2024 - 02:59 PM

This is called afocal photography - telescope and camera focused at infinity. The camera acts just as your eye does in making the final image.

It also acts just as your eye does in terms of the exit pupil of the telescope - namely if the entrance pupil of the camera is smaller than the exit pupil of the scope, you will effectively be stopping down the telescope - and if the camera is not right at the exit pupil, you'll get vignetting or blackouts. (A third complication is that the camera must be square to the optical axis, else you'll get spurious colors.)

A typical phone camera aperture is about 3mm I seem to remember. So your telescope will need to make a exit pupil of 3mm or less to use the complete telescope aperture. Meaning, medium to high power.

But the most difficult problem is the placement of the exit pupil of the eyepiece. You need a long eye relief eyepiece, and that means low power usually, meaning too large an exit pupil. You also need one with little "spherical aberration of the exit pupil", which rules out almost all wide field eyepieces. (Orthoscopics work best for me.)

The best eyepieces are thus those that combine sufficient exit pupil and eye relief. Most eyepieces don't work well. Using a regular camera with a much larger aperture eliminates the too-large exit pupil issue.

The upshot of all this is that, although it is the easiest form of photography through a telescope in principle, in practice it is hard to satisfy the constraints with most eyepieces and a cell phone camera. I have had good results with a pocket camera whose focus can be fixed at infinity, but never with a phone. Colored fringes are hard to avoid. The camera sees things you learn to not see visually.

-drl

The too large exit pupil is mostly a problem with reflectors, just like it is with the human eye. With refractors, it's not an issue. Yes, you're not getting the full light gathering power of the objective, but you're getting the brightest possible image at that f/ratio. I've used a 40mm Plössl on a 72mm f/6 refractor when doing afocal imaging with my smartphone. The scope is then working at 33mm aperture, so the eyepiece sees a 33mm f/13. This actually works wonders for the ol' Plössl, which delivers very crisp images right up to the edge.

With reflectors, it's best to use an exit pupil that matches the camera lens, or smaller. On my Zeiss Meniscas 150/2250mm it gives 56x and a 2.8mm exit pupil, just a hair smaller than the 3mm aperture of my smartphone camera. The camera is f/1.7, but works as f/1.96 on the Meniscas.

What this means in practice, is that I'm shooting at faster than f/2, faster than a RASA, on an f/15 Maksutov!!

This is not possible with larger aperture cameras, because you can't get an eyepiece with sufficiently large exit pupil, while still maintaining a decently large apparent field of view.

Most smartphone holders are utter crap, unfortunately, and have a very hard time keeping the camera accurately and stably mounted over the eyepiece. I have one that is decent, but unfortunately no longer in production, so I can't provide a link. I am toying with the idea of making something better.

Like you, I find simple eyepieces like Plössls and Orthos to be best. They are very sensitive to the right working distance between eyepiece and camera, though, but when you find it, the performance is very good right up to the field stop.

Once I got all the kinks worked out, I find smartphone afocal imaging to be very rewarding and quite simple and straightforward. The phone is a self-contained unit, so there's no need for external computers, power supplies, etc. It runs happily all night on a charge, taking hundreds of images.

Here are a couple of examples:

Mare Crisium in sunset, October 31st, 2023. Zeiss Meniscas 150/2250, 18mm ortho, 2,5x TV Powermate, Moto e7 phone, ProCam X Lite.

M27, May 12th, 2024. Taken with OnePlus Nord CE3 phone through Zeiss Meniscas 150/2250 at 56x magnification (40mm GSO projection eyepiece). 8 x 30 seconds at 6400 ISO.Stacked in DSS; contrast, brightness and colors adjusted with Windows Pictures.

M81 and M82, April 6th, 1:05 UT. 63/840mm Zeiss, 40mm GSO, 21x. 30 seconds at 6400 ISO. Image completely unedited. Equivalent focal length, 110mm f/1.7.

Clear skies!

Thomas, Denmark

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#6 deSitter

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Posted 17 July 2024 - 03:21 PM

The too large exit pupil is mostly a problem with reflectors, just like it is with the human eye. With refractors, it's not an issue. Yes, you're not getting the full light gathering power of the objective, but you're getting the brightest possible image at that f/ratio. I've used a 40mm Plössl on a 72mm f/6 refractor when doing afocal imaging with my smartphone. The scope is then working at 33mm aperture, so the eyepiece sees a 33mm f/13. This actually works wonders for the ol' Plössl, which delivers very crisp images right up to the edge.

With reflectors, it's best to use an exit pupil that matches the camera lens, or smaller. On my Zeiss Meniscas 150/2250mm it gives 56x and a 2.8mm exit pupil, just a hair smaller than the 3mm aperture of my smartphone camera. The camera is f/1.7, but works as f/1.96 on the Meniscas.

What this means in practice, is that I'm shooting at faster than f/2, faster than a RASA, on an f/15 Maksutov!!

This is not possible with larger aperture cameras, because you can't get an eyepiece with sufficiently large exit pupil, while still maintaining a decently large apparent field of view.

Most smartphone holders are utter crap, unfortunately, and have a very hard time keeping the camera accurately and stably mounted over the eyepiece. I have one that is decent, but unfortunately no longer in production, so I can't provide a link. I am toying with the idea of making something better.

Like you, I find simple eyepieces like Plössls and Orthos to be best. They are very sensitive to the right working distance between eyepiece and camera, though, but when you find it, the performance is very good right up to the field stop.

Once I got all the kinks worked out, I find smartphone afocal imaging to be very rewarding and quite simple and straightforward. The phone is a self-contained unit, so there's no need for external computers, power supplies, etc. It runs happily all night on a charge, taking hundreds of images.

Here are a couple of examples:

Mare Crisium in sunset, October 31st, 2023. Zeiss Meniscas 150/2250, 18mm ortho, 2,5x TV Powermate, Moto e7 phone, ProCam X Lite.

M27, May 12th, 2024. Taken with OnePlus Nord CE3 phone through Zeiss Meniscas 150/2250 at 56x magnification (40mm GSO projection eyepiece). 8 x 30 seconds at 6400 ISO.Stacked in DSS; contrast, brightness and colors adjusted with Windows Pictures.

M81 and M82, April 6th, 1:05 UT. 63/840mm Zeiss, 40mm GSO, 21x. 30 seconds at 6400 ISO. Image completely unedited. Equivalent focal length, 110mm f/1.7.

Clear skies!

Thomas, Denmark

Very nice! I got acceptable results with a Canon A590is pocket camera. I have a much better Nikon pocket camera which I haven't tried. I think because the whole process was an ordeal.

-drl

#7 LeeNixon

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Posted 18 July 2024 - 02:17 AM

The 500 rule comes from the days of photographic emulsion. It has a pixel scale built into it based on chemistry, and it is fixed. These days, pixels come in many sizes, and don't depend on chemistry. You know how big your pixels actually are, so use that information.

To find the trailing you can tolerate, start with what a trail means: the star moved over by at least one pixel. Then, it becomes rather simple. Simply find how long it takes for a star to move by one pixel. If you really, really don't like any oblong to your stars, make it half a pixel.

First, you are digiscoping, so everything behind the eyepiece creates its own pixel scale at the sensor. That depends on your objective focal length, and your pixel size, calculated as though there were nothing in front of the objective other than sky. Calculate how long it would take a star to move by one pixel with just the objective and the sensor. Then, because you are looking through an eyepiece, the star speed simply gets magnified by the amount of magnification. So, the time drops by a factor of the magnification.

Note that the time it takes a star to move by one pixel depends on the declination of the target. The celestial poles don't move at all, whereas everything moves the fastest at the celestial equator. To adjust for that, calculate the times at the celestial equator with 15.042 arcseconds per second of motion. Then, divide by cos(Dec). For the special case where field of view includes the celestial pole, everything will spin around that. So for that case, use the lowest Dec the field of view includes. The effect is the same as though the native pixel scale were divided by your magnification.

As an example, lets say your objective and your pixel size make a pixel scale of one arcsecond per pixel. You would get one pixels worth of star motion at the celestial equator in 1 [arcsecond per pixel] / 15.042 [arcseconds per second], or about 66.5 ms. Now, put that same setup behind an eyepiece that magnifies 10x. You would get one pixels worth of star motion at the celestial equator in 1 [arcsecond per pixel] / ( 10 x 15.042 [arcseconds per second]), or about 6.65 ms. If the target is at a Dec of 45 degrees, divide by cos (45) ~ 0.707, so it comes out to 6.65ms / 0.707 ~ 9.4 ms. It's the same result as with a pixel scale of the whole system of 0.1 arcseconds per pixel!

With a phone, you may not know either of your pixel size, or your phone objective's focal length. In that case, it's a lot easier to just work with the actual pixel scale of the whole system, as seen at the sensor. Take an image with a bunch of stars in it, then plate solve that image using astrometry.net. Other solvers will probably fail due to quality, or complete lack of knowledge of the pixel scale. Astrometry.net can solve just about anything. Once you have the pixel scale of your whole system (telescope plus eyepiece plus objective plus sensor), just work with the ordinary 15.042 arcseconds per second of motion and proceed from there.

#8 LeeNixon

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Posted 18 July 2024 - 02:18 AM

Wow! Thanks so much for the comprehensive reply. Much appreciated, though it will take me a while to get my head around it for sure.

#9 LeeNixon

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Posted 18 July 2024 - 02:20 AM

To calculate the focal length of the complete system when doing afocal imaging ("digiscoping"), just take the magnification of the eyepiece you're imaging through, and multiply it with the camera focal length.

Example: I use a 40mm eyepiece on a 2250mm focal length Maksutov. This gives 56x. The focal length of my camera lens in my phone is 5.24mm, according to manufacturer's specifications. The focal length is then 56 x 5.24 = 293.44mm

Clear skies!
Thomas, Denmark

Post was edited, because ButterFly explained things better than I did.

#10 LeeNixon

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Posted 18 July 2024 - 02:31 AM

Thanks for the response Thomas. Much appreciated.

#11 LeeNixon

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Posted 18 July 2024 - 02:32 AM

The too large exit pupil is mostly a problem with reflectors, just like it is with the human eye. With refractors, it's not an issue. Yes, you're not getting the full light gathering power of the objective, but you're getting the brightest possible image at that f/ratio. I've used a 40mm Plössl on a 72mm f/6 refractor when doing afocal imaging with my smartphone. The scope is then working at 33mm aperture, so the eyepiece sees a 33mm f/13. This actually works wonders for the ol' Plössl, which delivers very crisp images right up to the edge.

With reflectors, it's best to use an exit pupil that matches the camera lens, or smaller. On my Zeiss Meniscas 150/2250mm it gives 56x and a 2.8mm exit pupil, just a hair smaller than the 3mm aperture of my smartphone camera. The camera is f/1.7, but works as f/1.96 on the Meniscas.

What this means in practice, is that I'm shooting at faster than f/2, faster than a RASA, on an f/15 Maksutov!!

This is not possible with larger aperture cameras, because you can't get an eyepiece with sufficiently large exit pupil, while still maintaining a decently large apparent field of view.

Most smartphone holders are utter crap, unfortunately, and have a very hard time keeping the camera accurately and stably mounted over the eyepiece. I have one that is decent, but unfortunately no longer in production, so I can't provide a link. I am toying with the idea of making something better.

Like you, I find simple eyepieces like Plössls and Orthos to be best. They are very sensitive to the right working distance between eyepiece and camera, though, but when you find it, the performance is very good right up to the field stop.

Once I got all the kinks worked out, I find smartphone afocal imaging to be very rewarding and quite simple and straightforward. The phone is a self-contained unit, so there's no need for external computers, power supplies, etc. It runs happily all night on a charge, taking hundreds of images.

Here are a couple of examples:

Mare Crisium in sunset, October 31st, 2023. Zeiss Meniscas 150/2250, 18mm ortho, 2,5x TV Powermate, Moto e7 phone, ProCam X Lite.

M27, May 12th, 2024. Taken with OnePlus Nord CE3 phone through Zeiss Meniscas 150/2250 at 56x magnification (40mm GSO projection eyepiece). 8 x 30 seconds at 6400 ISO.Stacked in DSS; contrast, brightness and colors adjusted with Windows Pictures.

M81 and M82, April 6th, 1:05 UT. 63/840mm Zeiss, 40mm GSO, 21x. 30 seconds at 6400 ISO. Image completely unedited. Equivalent focal length, 110mm f/1.7.

Clear skies!
Thomas, Denmark

#12 LeeNixon

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Posted 18 July 2024 - 02:39 AM

Regarding phone holders, I current have one made by Viking (Birdwatching specialists) and I'm impressed by its build and function. It's also very intuitive and quick to set up. My only issue was that my phone camera lenses sit proud of the back of my phone, which meant the phone wasn't sitting parallel to the focal plane, but this was easily rectified by simply adding a spacer to the clamp that holds the phone.

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