For deep sky photography which requires a long exposure time, usually over an hour, the change in temperature during the imaging session affects the focus. To explain this phenomenon and control it, we will use two mathematical formulas:
- The expansion or contraction of the optical tube during a change in temperature
- Focus tolerance (MAP)
1- The expansion or contraction of the optical tube during a change in temperature
For every 1000 mm of physical length of the aluminum optical tube, a change of 1o Celsius is equivalent to expansion (or contraction if the variation is -1o Celsius) of the 0,023 mm tube.
The physical length of the optical tube is slightly less than the focal length of a telescope (from lens to focal plane) or Newton-type telescope (from primary mirror to focal plane). For these two optical tubes, we will consider the focal length of the tube, as it includes the focusing system (MAP) which is also sensitive to temperature changes (most of the time it is aluminum). For Schmidt-Cassegrain telescopes, concerning the MAP system, there are two passages of light in the optical tube to reach the focal plane. Here is an image visually explaining this statement:
In the image above, the light passes from the primary mirror to the secondary mirror and from the secondary mirror to the focal plane. So, for the purposes of simplifying the calculations, we will double the physical length of the tube, considering that this simple calculation will be a little longer than the effective length from the primary mirror to the focal plane through the secondary mirror.
Formula :
D = 0,023 / 1000 * LP
D = Expansion or contraction of the aluminum tube in mm per degree Celsius
LP = Physical length of the tube in mm
It should be noted that for carbon fiber tubes, the expansion or contraction of the tube is almost zero.
2- Focus tolerance (MAP)
Here is the formula for focus tolerance:
T = ± 8 x (F / D) ² x LO x FLO
T = MAP tolerance in mm
F = Focal length of the telescope or the telescope in mm
D = Diameter of telescope or telescope in mm
LO = Wavelength in mm
FLO = Accepted wavelength fraction
MAP tolerance for planets or high resolution photography
For an average wavelength of 0,0006 mm (0,6 microns), a wavelength fraction of 1/8 and less is required for high resolution photography. For a telescope with focal length (F / D) of 6, the MAP tolerance is therefore:
8x(62) x 0,0006 mm x (1/8) = ± 0,0216 mm
This means that from a perfect MAP, the MAP tolerance is 0,0216mm before or after this center point.
MAP's tolerance for the deep sky
Due to air turbulence and temperature changes during long exposure photography, the resulting MAP tolerance is at least double that shown for planet photography.
Here is a table showing the MAP tolerance in mm for different focal lengths:
| Focal (F / D) | 2 | 3 | 4 | 5 | 6 | 8 | 10 |
| MAP tolerance | |||||||
| ± mm planets | 0,0024 | 0,0054 | 0,0096 | 0,0150 | 0,0216 | 0,0384 | 0,0600 |
| Deep sky | 0,0048 | 0,0108 | 0,0192 | 0,0300 | 0,0432 | 0,0768 | 0,1200 |
We can see in this table that the tolerance of MAP is greater at f / 10 than at f / 2 for example (25 times greater!). This is due to the depth of field (or area of focus) which is greater in a closed focal length (f / 10) compared to a larger focal aperture (f / 2).
Impact of temperature change on MAP
Here is a table showing the impact of temperature variation, for different popular aluminum telescopes or scopes, on MAP quality:
Explanation of the columns:
| A, B and C | Accuracy expected in +/- of the MAP in mm over a long exposure session taking into account air turbulence and temperature changes. |
| D | Represents the expansion or contraction of the aluminum tube (mm) for each temperature change of 1o Celsius. See the formula above. |
| TO | Dividing column A by column D gives the maximum temperature variation for good air turbulence (0,4 "to 0,9" arc). |
| B / D | Dividing column B by column D gives the maximum temperature change for average air turbulence (1 "to 2,5" arc). |
| CD | Dividing column C by column D gives the maximum temperature variation for lean air turbulence (3 "to 4" arc). |
Impact of temperature change on MAP (except for HyperStar):
- To maintain a very good MAP (requires good air turbulence), the maximum temperature variation is 1,3o C to 6o C depending on the optical tube.
- To maintain a good MAP (average turbulence), the maximum temperature variation is 2,6o C to 12,1o C depending on the optical tube.
- To maintain an acceptable MAP (poor turbulence), the maximum temperature variation is 5,2o C to 24,2o C depending on the optical tube.
- Without going into all these details, we can therefore mention that a general temperature variation of up to 5o C will allow to maintain a good MAP corresponding to an average air turbulence (1 "to 2,5" arc) for telescopes of focal length f / 6 and more (f / 7… f / 10).
- For photography in HyperStar (also called Fastart), the constraints of MAP are too great to obtain an acceptable focus. As the images produced with this system have a very wide field of view, the exposure time per photo is very short (60 seconds compared to 10 minutes at f / 6,3) and therefore much less affected by temperature variations , there will not be a large visual impact caused by this poor MAP. The resulting image can be compared advantageously to that produced with a smaller focal length (f / 5 in the example).
conclusions
To respect the deviations indicated in the table of the impact of the change in temperature on the MAP, it is important to carry out a very precise focusing (to benefit from the deviations in +/-). I recommend you to use the software method (Max pixel and FWHM) or the one with the Bahtinov mask which eliminates variations due to air turbulence. All the details here.
For carbon fiber tubes, it is not useful to consult the table of the impact of temperature change on MAP, because the expansion of a carbon fiber tube is almost zero (only the temperature change of the MAP system will have to be considered and it will have an insignificant impact). It is therefore an important element to consider when purchasing an optical instrument.
On the other hand, for aluminum tubes, it is very interesting to consult the table. For example for my Edge HD 800 telescope with focal reducer, which is presented in the table at F / D 6,3, a temperature variation up to 4,8o Celsius will provide a good MAP and will be suitable for most nights (medium turbulence). Whereas it is rare that the temperature change during an imaging session exceeds 5o Celsius, I won't have to repeat the MAP often. Also, the telescope with the F / D 10 ratio is the least sensitive to temperature variations; interesting information to know.
We note, in the table, that telescopes or glasses made of aluminum with an open F / D ratio (f / 5 and more ie f / 4, f / 2) are very sensitive to temperature changes. This is explained by the depth of field which is less for these optical tubes. By focusing manually, it will be difficult to maintain a good MAP adapted for the majority of nights with average turbulence. Most of the time, you will get an acceptable MAP. To maintain a very good to good MAP, it would be necessary to re-focus regularly during the session, which represents a difficult task. One solution is to automate the MAP. For details on the material to be used as well as an estimate of the costs, see the Focusing the CCD camera and go to section Automate focus. Of course, another simpler and less expensive solution is to use a carbon fiber tube for these open instruments.
If your aluminum optical tube is not shown in the table, I recommend that you take the time to do your own calculations. This will allow you to better understand the sensitivity of your optical instrument to changes in temperature. For the physical length of your tube, use a tape measure to establish the physical length of the tube including your focusing system. If your tube is a Schmidt-Cassegrain type, remember to double the physical length of the tube (see explanation above).
All these theoretical calculations make it possible to estimate the impact of the change in temperature on the focus for aluminum tubes. In reality, there are several other factors which influence the quality of MAP (the collimation, the precision of the frame in autoguiding, the dilation of the lenses or mirrors, the temperature of the equipment…). You must therefore validate everything in a real situation with your own equipment. When there is a temperature change of more than 5o Celsius, compare the last image taken with the first. This evaluation will allow you to judge the relevance of carrying out a new focus.
Richard Beauregard
The Sky Astro-CCD
To learn about focusing methods:
Focusing the CCD camera
References :
http://jalle-astro.fr/wp/la-mise-au-point/
http://www.regnier-schmit.net/faqastrocam/1005/
Richard Beauregard
Sky Astro - CCD
Revise on 2021/11/03