Magnification of a telescope coupled with a DSLR camera

[Panama Hat & Camera]

I was wondering how to calculate the prime magnification of a telescope attached to a DSLR camera and I found this interesting website, that has a DSLR Calculator for Astrophotography.
http://www.astro.shoregalaxy.com/dsl...htm#calculator

According to this other website, the prime magnification is calculated for a 35 mm film camera by dividing the focal length of the telescope by the film plane of the camera which is 43.27 mm (this value is the diagonal of a 35mm film or a full frame sensor).
http://www.skyatnightmagazine.com/fo...tion-t752.html

The results obtained by the two methods are the same and we can say that, in general:
Magnification = Telescope focal length / Camera sensor diagonal

Cheers,
Antonio.

[xpatUSA]

I was wondering how to calculate the prime magnification of a telescope attached to a DSLR camera and I found this interesting website, that has a DSLR Calculator for Astrophotography.
http://www.astro.shoregalaxy.com/dsl...htm#calculator

According to this other website, the prime magnification is calculated for a 35 mm film camera by dividing the focal length of the telescope by the film plane of the camera which is 43.27 mm (this value is the diagonal of a 35mm film or a full frame sensor).
http://www.skyatnightmagazine.com/fo...tion-t752.html

The results obtained by the two methods are the same and we can say that, in general:
Magnification = Telescope focal length / Camera sensor diagonal

Cheers,
Antonio.

Interesting. For 300mm (my longest telephoto lens) on my Sigma SD15, I get magnification about 12 and one pixel = 5.39 arc-sec.

Making the Moon quite small in my frame ...

https://sites.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect2/lecture2.html

The calculator seems quite simple:

http://www.astro.shoregalaxy.com/dsl...htm#calculator

function calculateArcSecPix()
{
    var sensorw = document.getElementById("Sensor Width").value;
    var sensorh = document.getElementById("Sensor Height").value;
    var maxres = document.getElementById("Max Res").value;
    var focleng = document.getElementById("Focal Length").value;;
    var thisF = sensorw * 3438/focleng;
    var thisF2 = sensorh * 3438/focleng;
    var thisF3 = sensorw * 3438/focleng * 60/maxres;
    var thisF4 = focleng/Math.sqrt(sensorw * sensorw + sensorh * sensorh);
        
    document.getElementById("thisResult").value = thisF;
    document.getElementById("thisResult2").value = thisF2;
    document.getElementById("thisResult3").value = thisF3;
    document.getElementById("thisResult4").value = thisF4;
    document.getElementById("thisResult5").value = thisF5;
}

For 'thisF3', the constant 3438 converts the pixel pitch/focal length into arc-minutes, then x 60 = arc-seconds.

https://spacemath.gsfc.nasa.gov/weekly/5Page61.pdf
.

[Panama Hat & Camera]

Ted,
Thanks for the code of the calculator.
I had prepared an Excel Spreadsheet and there were some very minor differences between the results of my spreadsheet and the calculator. This happened because I used the trigonometric function "arc tangent" in my calculations instead of small angle approximation (the differences are negligible).

With the calculator, I get the following results for my cameras:

- Canon SX50 HS (4.3-215 mm lens, set @ 215 mm)
One pixel = 1.48 arc-sec;
Magnification = 28.0 X.

- Nikon D5300 and the Nikkor 18-300 mm lens (set @ 300 mm)
One pixel = 2.69 arc-sec;
Magnification = 10.6 X.

Thanks for the links about angles (from University of Alberta and from NASA).

Cheers,
Antonio.

[Otavio]

Very interesting, Antonio! I suppose the DSLR Calculator for Astrophotography can also be used to play with the features of the LORRI telescope, have you tried it?

[george013]

Ted,
Thanks for the code of the calculator.
I had prepared an Excel Spreadsheet and there were some very minor differences between the results of my spreadsheet and the calculator. This happened because I used the trigonometric function "arc tangent" in my calculations instead of small angle approximation (the differences are negligible).

With the calculator, I get the following results for my cameras:

- Canon SX50 HS (4.3-215 mm lens, set @ 215 mm)
One pixel = 1.48 arc-sec;
Magnification = 28.0 X.

- Nikon D5300 and the Nikkor 18-300 mm lens (set @ 300 mm)
One pixel = 2.69 arc-sec;
Magnification = 10.6 X.

Thanks for the links about angles (from University of Alberta and from NASA).

Cheers,
Antonio.

I've never thought of telescopes so I have no idea where you're talking about. But in your example is written "enter camera & telescope details" and you use the focal length of your lens. Are telescope and lens synonym?

George

[Panama Hat & Camera]

George,
Telescope and lens are not synonymous. Lenses are part of a telescope.
There are three basic types of optical telescopes: refractors, reflectors and catadioptrics. The part of the telescope that gathers the light, called the objective, determines the type of telescope. The objective gathers light and bends it into focus. The eyepiece (ocular lens) brings the bright image from the focus and magnifies it to the size of eye's pupil.
A refractor telescope uses a glass lens as its objective. The glass lens is at the front of the telescope and light is bent (refracted) as it passes through the lens. The objective of a refractor telescope is similar to a fixed focal length telephoto lens of a DSLR camera.

The visual magnification of the field of view through a telescope can be determined by the telescope focal length divided by the eyepiece focal length. When a DSLR camera is coupled to a telescope, the objective of the telescope becomes the lens of the camera. A DSLR camera coupled to a telephoto lens is similar to DSLR coupled to a small telescope. Thus, the DSLR Calculator for Astrophotography can be used for a telescope or for a telephoto lens.

The DSLR Calculator for Astrophotography uses the "small angle approximation", that gives satisfactory results for telescopes and most telephoto lenses. For short telephotos, normal and wide angle lenses, it is better to use the trigonometric function "arc tangent".
Cheers,
Antonio.

[Panama Hat & Camera]

Thanks for asking, Otavio.
Actually, the DSLR Calculator for Astrophotography applies perfectly to the LORRI telescope, as we can see below.

According to the document ssr-lorri.pdf (see more at www.boulder.swri.edu/pkb/ssr/ssr-lorri.pdf), LORRI is a narrow angle (field of view = 0.29°), high resolution ( 4.95 μrad/pixel), Ritchey-Chrétien telescope camera with a focal length of 2630 mm (f/12.6) and a 1024 × 1024 pixel (optically active region) sensor (see the thread The camera of the farthest photographer from the earth for more informations).

The following results were obtained from the calculator:
Arc of the sky (width and height) = 17.386 minutes;
Arc / pixel seconds = 1.0187;
Magnification = 139.8 X.

Let's do some calculations:
17.38 minutes / (60 minutes / 1 degree) = 0.29 degrees (OK!);
17.38 minutes / (60 minutes / 1 degree) x (3.1416 rad / 180 degrees) / 1024 pixels = 0.00000495 rad / pixel = 4.95 μrad / pixel (OK!)

[videofame]

Hi Panama Hat & Camera

I was wondering how to calculate the prime magnification of a telescope attached to a DSLR camera and I found this interesting website, that has a DSLR Calculator for Astrophotography.
http://www.astro.shoregalaxy.com/dsl...htm#calculator
Cheers,
Antonio.

The website you refer to in above reference is no longer working. Any other ideas you might have for an app or quick view website to do this calculation: "Magnification of a telescope coupled with a DSLR camera".

Magnification = Telescope focal length / Camera sensor diagonal

I have tried what you suggested in above statement which is: taking camera lens 300mm focal length/43.7mm diagonal of my full frame 35mm camera sensor.
it says 6.865 which I'm guessing your thinking is Magnification. However I need to know what is the angular size in arc seconds. I'm trying to discover what deep space objects and their related apparent arc second sizes would be best suited for my camera lens.