WHAT ARE THE EFFECTS OF THE CENTRAL OBSTRUCTION ?

What is obstruction ?

The obstruction of a reflector is represented by its secondary mirror (and its support) which blocks the central part of the optical path.

The amount of obstruction can vary from one telescope to another. It depends on its optical design (Newtonian, SCT, etc.) and also on the method of construction (folded path, multiple reflections, etc. Obstruction usually is expressed as a percentage of the diameter of the telescope, usually from 15 % to > 35 %. Some specialized instruments, like the ones dedicated to deep-sky astrophotography (Schmidt Cameras), can be obstructed more than 40 %.

Some telescope manufacturers list the value of the obstruction of their reflectors as a percentage of the collecting surface of the instrument instead of the percentage of its diameter. In this case, the surface obstruction can be computed from the obstruction diameter by calculating its square. Example: a diameter obstruction of 20 % (40 mm on a 200 mm) corresponds to a surface obstruction of 4 % (square of 0.20). Conversely, a surface obstruction of 10 % corresponds to a diameter obstruction of 32 % (square root of 0.1). Other manufacturers specify only the minor diameter of the elliptical secondary mirror instead of the total diameter of its support. This is dubious since it under-estimates the total optical path obstruction.

The effects of obstruction are twofold: First, it limits the amount of light received by the instrument, and, secondly, it modifies the contrast and resolution of the image.

The decrease of light received by the instrument corresponds to its equivalent surface obstruction. This is relatively minor, for example, a telescope with an obstruction of 20 % loses only 4 % of its light gathering ability, while an obstruction of 33 % leads to a light loss of only 11 %. Thus, it is clear that, even with large obstructions, the relative loss of light is small: a 250 mm reflector obstructed at 34 % receives the same amount of light than an unobstructed 235 mm telescope.

What are the effects of obstruction on the diffraction pattern ?

The presence of obstruction modifies the diffraction pattern (Airy pattern) of the optical instrument. This is most notable at high magnification, a star appears as a central disk (false disk) surrounded by rings of decreasing brightness (figures below). The obstruction has the effect of decreasing the amount of light at the center of the disk (whose diameter is slightly decreased), and increasing the illumination in the surrounding rings. The figures below depict the appearance of the Airy pattern for obstructions of 0 %, 20 % and 33 %.


Without obstruction


20 % obstruction


33 % obstruction

Note that these images are plotted in a logarithmic scale to agree with the way that human vision will perceive them. Also, note that as the obstruction is increased from 0 % to 33 %, the maximum intensity of the first diffraction ring increases from 1.7 % to 5.4 % of the maximum intensity of the central disk. It should be pointed out that the central disk does not merge with the first diffraction ring, this is one of the "Old wive's tales" that simply are not true and are against the laws of physical optics. The figure below depicts the family of Point Spread Functions (PSF curves) that correspond to these obstructions.

What are the effects of obstruction on image contrast ?

The MTF curve below shows that image contrast is modified in a complex manner. The figure shows that contrast decreases compared to the unobstructed telescope, but only for low and medium frequencies (left part of the curve). Interestingly enough, the contrast does not decrease at high frequencies, it actually increases by a slight amount .

The figure below depicts curves corresponding to reflectors obstructed at 20 % and 33 %. The extension of the left part of each curve shows equivalence to an unobstructed telescope, for contrast in the low frequency region. It shows that in these frequencies a reflector with an obstruction of 33 % is equivalent to an unobstructed instrument whose diameter is 33 % less (170 mm for 250 mm). Also, a reflector with an obstruction of 20 % is equivalent to an unobstructed instrument whose diameter is 15 % less (210 mm for 250 mm).

An empirical mathematical rule deduced from these results shows that an instrument of diameter, D and obstruction d, is equivalent to an unobstructed instrument whose effective diameter Deff is:

Deff = D - d (again in the low frequency region)

(this formula is somewhat pessimistic for small obstructions).

To examine the effects on resolving power of a telescope, we must consider two cases:

1) high contrast structures: Moon, double stars, Cassini division, shadow of a ring or a satellite, edge of a planet. Since these resolution limits are on the right part of the MTF curve, these are not modified by obstruction.

2) low contrast structures: surfaces of Mars, Jupiter and Saturn. The resolution limit is situated at a lower frequency than in the first case. For details of very low contrast, this limit can be placed before the intersection of the curves. In this case, it is lower for the obstructed instrument. Then, as for the contrast in low frequencies, the resolution of the instrument is equivalent to those of an unobstructed telescope whose diameter is Deff.

The fact that the resolution limit is to the left or to the right of the intersection of the curves (and therefore the fact that there is a reduction of the resolution or not) depends on the intrinsic contrast of the object (which can vary according to the wavelength: For example, Jupiter has more contrast in the blue than in the red). It also depends on the technique: CCD, photography or visual observation (the contrast threshold differs: about 2 % for the eye in good lighting conditions, probably 0.5 % in CCD). No general rule can be given about the loss of resolution on low contrast surfaces. Nevertheless, the effective resolution is at least the resolution of an unobstructed instrument of diameter Deff.

These results are valid only if the instrument is of good optical quality and properly collimated. If not the case, then the MTF curve is compressed, the resolution limit is lowered and the loss of resolution affects all objects, including high contrast objects like the Moon.

The spider (secondary mirror mounting), although it creates diffraction spikes on bright stars, has no visible influence on the contrast of lunar and planetary images. Thus, for high resolution, it is not necessary to use tricks like curved (arced) arms.

What are the effects of obstruction on planetary and lunar images ?

The lunar and planetary images below (left column) display what would be displayed on an unobstructed 150 mm telescope during excellent seeing conditions. The next columns contain computer simulations of obstructions of 20 % and 33 % respectively, as applied to this same instrument.

Without obstruction

20 % obstruction

33 % obstruction

The modification of the image due to the obstruction of 20 % is barely noticeable. Such an obstruction can be considered as nearly negligible, it is probably difficult to differentiate in practice from a zero obstruction. The obstruction of 33 % has a more pronounced effect on the global contrast. However, note that there is still high relief detail on lunar craters and rilles, for these images the resolution power of the instrument has not changed. On the other hand, note that details with low contrast (surfaces of Jupiter and Saturn), seem somewhat washed out, indicative of a decrease in resolution.

Conclusion

The effects of obstruction are:

1) the general contrast of the image is lowered, the instrument (diameter D, obstruction d) has approximately the same efficiency as an unobstructed instrument of diameter Deff = D - d

2) the resolution power is not modified on high contrast structures:
Moon, double stars, Cassini division, shadow of a ring or a satellite, edge of a planet,...

3) the resolution power may be lowered on low contrast objects: surfaces of Mars, Jupiter and Saturn. The effective resolution depends on the contrast of the object and the technique used, but note that it is at least the resolution of an unobstructed telescope of diameter Deff

Results are summarized in the following table:

Reflector diameter
33 % obstruction

Equivalent diameter of a refractor about global contrast

Equivalent diameter of a refractor about planetary resolution

Equivalent diameter of a refractor about lunar resolution

Equivalent diameter of a refractor about amount of light (2)

300 mm

200 mm

200 to 300 mm (1)

300 mm

280 mm

250 mm

170 mm

170 to 250 mm (1)

250 mm

235 mm

225 mm

150 mm

150 to 225 mm (1)

225 mm

210 mm

200 mm

130 mm

130 to 200 mm (1)

200 mm

190 mm

150 mm

100 mm

100 to 150 mm (1)

150 mm

140 mm

(1) : depends on the contrast of the object and the technique used
(2) : with identical transmission coefficients of the optics

The obstruction, even if it effects planetary contrast and resolution, does not preclude high resolution. Thus, on planets, the obstruction alone does not make a 250 mm reflector with 33 % obstruction inferior to an unobstructed 170 mm refractor. On the Moon, the reflector maintains its entire resolution capability.

However, it is better to have an instrument with low obstruction than one with large obstruction. But it would not make sense to focus only on obstruction and neglect all other considerations, and conclude that a telescope with a low obstruction is automatically better than a telescope with a higher obstruction. Other factors like misalignment, insufficient thermal equilibrium or bad seeing, often dominate and, in these cases, obstruction becomes a negligible phenomenon. Even if a mirror performs well at the Foucault test, and is being used with a small obstruction, this does not always guarantee high resolution results.

I have heard statements like: "the obstruction lowers the resolution power ", or, "an obstructed instrument loses 50 % of its resolution power ", "an instrument obstructed at 33 % is unusable in high resolution " or "the obstruction has less effects in CCD imaging than in visual". These statements are mostly incorrect, they are contradicted by diffraction laws and by observational experiments. It is quite possible that these assertions come from observations of other effects, and are incorrectly attributed only to obstruction issues. As previously stated, many amateur Newtonian reflectors suffer from gross misalignment (even if their owners do not agree), which lead to a deterioration of performance well beyond the aberrations caused by any obstruction. The only valid way of seeing the real effects of obstruction is to measure a single instrument (refractor or Newtonian with low obstruction) and then artificially obstruct it with carefully constructed disks of varying sizes, thus suppressing all the other aberrations that would otherwise mask the measurement.

Some final points ....
For an amateur who constructs his own reflector, it may be tempting to want to design a system and minimize the size of the secondary mirror. If this mirror is undersized, the periphery of the light beam is lost, leading to a light decrease and an effective increase in obstruction (the opposite of the goal !). Also, many (industrial or home-made) mirrors suffer from defects at their periphery (turned edge). In this case, using the very edge of them can cause a deterioration of performance beyond what would have been caused by a small increase in the size of the central obstruction.