PSF size


　According to Rayleigh's formula, a resolution of a telescope is written as

ε　=　1.22 λ / D [ rad ]
λ：Wavelength
D：Diamiter of telescope

and its reslution on CCD can be written as

δ　=　f ε　= f　1.22　λ　/　D　=　1.22　Fno　λ
f：focal length
Fno: Ratio between D and f

therefore, PSF size is determined by Fno and wavelength, not diameter.

We are being bothered by atomospheric turbulance, and star images are not so sharp as theorical images. Considering the scintilation, a term of seeing, δ’, is added to resolution formula. The scintilation on CCD is propotinal to forcal length and scintilaion, then it is written as

δ’=　f　tan（ seeing ）= f seeing
seeing : seeing [ radian ]

　Finally, the resolution image with scintilation is written by

δ　=　δ　+　δ’=　1.22　Fno　λ　+　f　tan( seeing ) = 1.22　Fno　λ　+　f　seeing

For example, the PSF size at 550nm wavelength and 2.0 arcseconds seeing

δ　=　0.671　Fno　+　f　tan(2")

The next list is calculated by this formula, Tanaka's resolution formula


1000120014001600180020002400260028003000f.l.
100 16.4 19.6 22.9 26.2 29.4 32.7 39.3 42.5 45.8 49.1
160 13.9 16.6 19.4 22.2 24.9 27.7 33.3 36.0 38.8 41.6
200 13.0 15.6 18.2 20.8 23.4 26.0 31.3 33.9 36.5 39.1
250 12.4 14.8 17.3 19.8 22.2 24.7 29.7 32.1 34.6 37.1
300 14.3 16.7 19.1 21.4 23.8 28.6 31.0 33.4 35.7
400 18.2 20.4 22.7 27.3 29.5 31.8 34.1
600 25.9 28.1 30.2 32.4
Diameter

PSF size [ micron meter ], Diameter and f.l. [ mm ]


　


2003,May 21st originally in Japanese
2003,June 13st in English

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