Астрорасчеты для камер

CCD arc-sec/pixel & Focal Ratio

The formula for arc-sec per pixel is:

 Focal length of scope CCD pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Calculated arcsec/pixel

Alternatively you can measure the size of an imaged object in pixels, and divide that objects known size in arc-seconds by the size in pixels.

 Object size in arc secs Image size of object in pixels Calculated arcsec/pixel

Solving for focal ratio, this becomes:

 CCD pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Image arcsec / pixel Scope aperture (mm) Calculated focal ratio

You can use this formula to get a reasonably accurate focal ratio from any image where you know the angular size of an object (or angular distance between two stars).

Or if you want the focal length used for an image and know the angular size of the object imaged:

 CCD pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Object size in pixels Object size in arc seconds Calculated focal length

CCD Planetary Critical Sampling

Use this formula to calculate the minimum focal length required to fully sample a high resolution image with any particular CCD.

This is based on the assumption of perfect seeing and the Airy disk being the limit of resolution. For planetary imaging using 'lucky' imaging short exposure techniques this is a reasonable assumption. For long exposures the FWHM value for any particular night would be a better measure of the resolution obtainable.

I have made the assumption that adequate sampling requires the pixel spacing to be three times greater than the scopes resolution (forget Nyquist!)

 Light Colour Green Red Blue user entered Wavelength (nm) Scope aperture (mm) CCD pixel size (microns) Calculated focal ratio Calculated focal length

Focal Reducers

Use this formula to calculate the resulting focal ratio when using a focal reducer:

And this one to calculate the amount of in-focus required by that set-up:

 Focal Reducer Celestron 0.63x Meade 0.33x William Optics 0.8x ATiK 0.5x user entered CCD-FR distance (mm) FR focal length (mm) Focal ratio of scope Calculated focal ratio Calculated in-focus required*

Where

a = Distance of CCD from focal reducer
b = Focal length of FR
c = Focal ratio of scope

The Meade/Celestron focal reducers have the following focal lengths.
[note: Around 2006 Meade manufactured some 0.63 focal reducers with a focal length of around half what they should be making them unsuitable for use with SLR cameras or filter wheels, any marked "Japan" are OK, as are later "China" ones.]
:

FR 0.33x focal length = 85mm
FR 0.63x focal length = 285mm

William Optics 0.8x FR focal length = 260mm

ATIK 0.5x FR focal length = 80mm

* Note that the in-focus figure assumes that the FR-CCD spacing is added to your physical imaging train length (as when using the Meade/Celestron FR's with spacing tubes). If you are using a FR like the ATIK that is fitted internally, then you have to add the FR-CCD spacing to this figure (to make it smaller). If you are using a FR like the Meade/Celestron then you will have to subtract the depth of the FR itself to this figure (to make it a larger negative number).

If you are troubled by dust shadows on your CCD images you can calculate the distance that the dust particle is in front of the CCD with the following formula:

 CCD pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Imaging system focal ratio Diameter of dust shadow (pixels) Calculated distance from CCD (mm)

Where:

Dist = Distance from CCD surface in mm
p = CCD pixel size in microns
f = Focal ratio of imaging system
d = Diameter of dust shadow in pixels

CCD Filter Reflections

Want to know where those annoying reflection disks around stars are coming from?...

To calculate this

 CCD pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Imaging system focal ratio Diameter of reflection (pixels) Calculated distance from CCD (mm)

Where:

Dist = Distance from CCD of reflection surface in mm
D = Diameter of reflection disk in image in pixels
P = CCD pixel size in microns
FR = Focal ratio of imaging system

Signal to Noise Ratio

A simplified formula for calculating the signal to noise ratio in an image is:

where:

S = total nebula signal
B = total background signal
D = dark current
RN = read noise from bias frame
n = number of sub-exposures

Critical Focus Zone

Calculate the length of the zone in which the focused image of a star is smaller than the size of its Airy disk.

which simplifies to:

For CCD cameras, if we take a 2x sampling ratio:

where:

λ = wavelength of light

 Light Colour Green Red Blue user entered Wavelength of light Focal Ratio Camera pixel size (microns) Pixel binning 1x1 2x2 3x3 4x4 Critical Focus Zone CCD Focus Zone

Note that because at low f/ratios the size of the Airy disk becomes significantly smaller than typical CCD pixels sizes I have introduced a value for the CCD Focus Zone. The value for the CCD focus zone takes the larger value of the CFZ, or where the Airy disk is half the effective pixel size (2x under sampling ratio) the CCD focus zone value defined above. For small focal ratios the CFZ gives a misleadingly small figure for imagers.