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energy loss of spherical aberration. The answer is an aperture about 32% obstructed.1

However, we must examine the frequency responses of these two situations to see where the blanket statement of equivalence breaks down. The corresponding MTFs are plotted in Fig. 3-6. We see that they are roughly the same for spatial frequencies about half of the Rayleigh criterion. For 200-mm telescopes, these two optical situations show periodic planetary detail having spacings of roughly 1 to 2 arcseconds equally well.

The response at higher and lower spatial frequencies are different, however. At the high end, the obstructed aperture delivers better contrast than 1/4 wavelength of spherical aberration. Surprisingly, it even performs better than a perfect aperture.

Fig. 3-6. Comparing the nitration of simple spherical aberration and central obstruction.

At the low end, the obstructed aperture has a higher MTF for spatial frequencies until bar separations are more than eight times the Rayleigh criterion. For a 200-mm aperture, details separated between 2 and 5 arc-seconds are shown better by the obstructed aperture. On coarse details separated more than 5 arcseconds the two contrasts are pretty much the same, but still slightly less than the perfect aperture.

Thus, for low-power, deep-sky viewing, '/4 wavelength of spherical aberration is slightly worse than the obstruction. For double-star separation at or slightly beyond the Rayleigh criterion, the obstruction wins again. Only

Fig. 3-6. Comparing the nitration of simple spherical aberration and central obstruction.

Fraction of maximum spatial frequency

Fraction of maximum spatial frequency

1 See Table 10-1.

for intermediate spatial frequencies is the frequency response about the same or inferior in the obstructed instrument.

The obstruction may be adjusted until the transfer functions are a little closer (the shadow diameter would be nearly 35% of the full aperture), but all-inclusive comparisons should not be made without caution.

Fraction of maximum spatial frequency Fig. 3-7. MTFs associated with various amounts of defocusing.

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