## Vwv

before after a)

Fig. 3-4. Target intensity of modulated brightness: a) before filtering, b) after filtering. Note: the energy of the image is still the same, but in b) it is less modulated. The target is not actually corrugated—this is just a way of indicating surface brightness.

appearance (0.5 = —3 dB, 0.25 = —6 dB, etc.). If this plot were of an audio system, the bottom axis would go from 0 to well beyond 20,000 Hz. In fact, easily audible sounds would occupy the lowest '/.10 of the spectrum. Similarly, much interesting detail in sky objects is at low spatial frequencies where the transfer function is high. This plot emphasizes the highest frequencies where the transfer is likeliest to fall down.

The maximum spatial frequency (on the far right, 1.0 on the chart) is with 0min representing a separation angle slightly narrower than the 1.22X/D angle associated with the radius of the diffraction disk, also known as the Rayleigh resolution criterion. Here, a bar separation equal to the radius of the diffraction disk would occur at 1/1.22 = 0.82 of the maximum spatial frequency (marked with bar).

Fraction of maximum spatial frequency

Fig. 3-5. The best-case unobstructed circular MTF. Incoherent lighting of the target is assumed.

Fraction of maximum spatial frequency

Fig. 3-5. The best-case unobstructed circular MTF. Incoherent lighting of the target is assumed.

If we wish to use the notation that is more associated with cameras, the maximum spatial frequency at the focal plane (where F is the focal ratio) is

For example, if the aperture has a diameter of 200 mm and a focal length of 1200 mm and the wavelength considered is 550 x 10-6 mm, then S'max is 303 cycles/mm or lines/mm. Smax in angle notation for a 200 mm aperture would be 364,000 cycles/radian or 1.76 cycles/arcsecond.

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