# Resolution, field of view, etc

This page presents some simple calculations about the resolving power of my telescope and the field of view when used with my camera. This is useful to know when using the instruments.

There is also information about the wavelength sensitivity of the camera.

## Camera pixel size

Camera: EOS 5D MkII

Full 35mm frame, which means 36 x 24mm, which equates to pixels:
Width = 5616px = 36mm => 0.00641 mm/px
Height = 3744px = 24mm => 0.00641 mm/px
(ie, 6.4 micron pixel size)

## Telescope resolution

Telescope: 254mm f/4.8
=> focal length F = 1219mm
Rayleigh resolving power = 138 / 254 = 0.543 arcsec
(ie, the minimum separation of 2 stars that could possibly be seen as separate, under ideal conditions)

Angle subtended by a 6.4 micron camera pixel at prime focus of telescope (configuration [A]):
0.00641 / 1219 = 5.2575e-6 radians = 3.0124e-4 degrees = 1.084 arcsec
So 2x Barlow on camera (configuration [B]) would match the Rayleigh resolution exactly. However, that would place the two closest stars on neighbouring pixels and so would still not enable them to be seen as separate. In practice of course it is not possible to keep the camera/telescope steady enough during an exposure and well enough focussed to image a star as a single pixel.

## Field of view at prime focus

So the theoretical angular size of full frame in configuration [A]:
Width 36mm: angle = 2 x atan (18 / 1219) = 1.692 degrees
Height 24mm: angle = 2 x atan (12 / 1219) = 1.128 degrees
which equates to 3319.15 px/deg.

Compare that with measurements made by calibrating an image of the Pleiades with a star chart generated by GRIP from Hipparcos and Tycho data:
Width 1.717 degrees
Height 1.144 degrees
which equates to 3271.5 px/deg.

The difference (47 px/deg) could be due to the fact that the focal ratio of the telescope is not exactly 4.8. That should be measured. Then I would expect the theoretical value for the scale to approach the calibrated measurement.

Knowing the scale factor from pixels to degrees it becomes very simple to, for example, measure the speed of a comet.

## Field of view for various lenses

Focal length
f (mm)
Full size
24 x 36 mm
APS-C size
15 x 22.5 mm
1577.3° x 100.4°53.1° x 73.7°
2061.9° x 84.0°41.1° x 58.7°
2551.3° x 71.5°33.4° x 48.5°
5027.0° x 39.6°17.1° x 25.4°
7518.2° x 27.0°11.4° x 17.1°
10013.7° x 20.4°8.6° x 12.8°
2006.9° x 10.3°4.3° x 6.4°
3004.6° x 6.9°2.9° x 4.3°
4003.4° x 5.2°2.1° x 3.2°
5002.7° x 4.1°1.7° x 2.6°
8001.7° x 2.6°1.1° x 1.6°
10001.4° x 2.1°0.9° x 1.3°
12001.1° x 1.7°0.7° x 1.1°

The largest focal lengths here are for telescopes rather than camera lenses of course.

### A camera field of view calculator

(eg, Barlow lens)

## A simple check of the effective focal length

The effective focal length of the photographic set-up can be measured by using GRIP. Photograph something with a known angular dimension (eg, the separation of a double star) and measure its size in pixels in the image. One of my first photos was of M57, the planetary nebula in Lyra (see next page). That was taken through a 2x Barlow lens (configuration [B]). The documented size of M57 is 1.8 x 1.4 minutes of arc ('). In GRIP use the straight line option on the measurement menu of the image:

That shows that an angular dimension of 1'.4 ends up as 150px on the image. The image size (in my case) is 5616 x 3744 px and the detector (in my case) is 36mm x 24mm. So 1'.4 becomes 36 x 150 / 5616 = 0.962mm on the detector. The effective focal length, F is then given by the formula

F = w / 2.tan (a/2)

where a = angle subtended (remember to convert to radians: 1 radian = 57.3 degrees) and w = width on detector (in the same units as F). In my example this gives F = 2380mm. This means that the Barlow lens is multiplying my telescope's focal length by 2380 / 1219 = 1.95. I repeated this on the other dimension of the nebula and got the same result, within the number of significant figures quoted.

## Measuring the field of view

It might be thought that the best way to measure the field of view would be to stop the motor drive on the telescope mount and time the movement of a bright star from one side of the camera's viewfinder (or live view screen) to the other. Unfortunately neither of those is likely to show the full extent of a photograph. So instead use the calibration facilities of GRIP. On the measurement menu again, select calibrate:

Having done that, measure the whole image (simply select whole image from the measurement menu). The resulting display will show the image size in the calibrated units.

In my case that showed that the field of view in the negative projection set-up described above is 50' x 33'.

## Wavelength sensitivity

I had always assumed that I would not be able to photograph the Horsehead Nebula with an unmodified DSLR because it would not be sensitive to the Hydrogen Alpha line (656nm). But when I photographed Zeta Orionis (result here) I found that the Horsehead showed up with quite a short exposure. So I was curious as to where the Hα line lay in the sensitivity range of the camera.

Using a home-made slit and some plastic replica diffraction grating (1000 lines/mm) I photographed a solar spectrum. I measured the relative positions of the major lines in GRIP and that enabled me to annotate the spectrum as shown on the left.

GRIP also produced the following profile from which I reckon that the camera covers a range from about 415nm to 685nm.

The numbers along the axis of the graph are pixels vertically in the image on the left. The slit is at about 10 pixels.

The black trace on the graph is the root sum of squares of the RGB traces.

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