Lurie-Houghton Telescope Design
First corrector lens (positive, BK-7 glass)
(D = 10in, stopped down to 9.8in)
R1 = 72.6in
T1 = 0.608in
R2 = -208.0in
|Air space between corrector lenses||
T2 = 0.11in
Second corrector lens (negative, BK-7 glass)
(D = 10in, stopped down to 9.8in)
R3 = -72.6in
T3 = 0.375in
R4 = 208.0in
|Air space between corrector and primary mirror||
T4 = 37.5in
Spherical primary mirror (Astrositall)
(D = 10in)
|Air space between primary and secondary mirror||
T5 = -34.6in
|Flat diagonal mirror (D = 3.1in)||
R6 = 0
|Distance from optical axis to focal plane||
T6 = 10.217in
|Radius of curvature of focal plane||R7 = 149in|
This drawing shows the details for the corrector lenses. I'm using AutoCAD Release 14 for all of the design drawings. Besides 2D drawings, I'm also modeling all of the parts using 3D solids. By doing this I can see how the parts fit together and it allows me to create 3D renderings.
How does the Lurie-Houghton compare to an equivalent Newtonian?
The following figures compare the performance of the Lurie-Houghton telescope I designed to a Newtonian telescope with the same aperture and focal ratio.
The spot diagrams
This first set of diagrams are spot diagrams. They show how the light is focused. The small black circle in the center of the spot diagrams represent the diffraction limit for a 9.8" aperture. It is the same size as the airy disc seen using a high power eyepiece. Ideally, all the light entering the telescope should focus within the diffraction limit. This is referred to as being diffraction limited. Most commercial telescope vendors will state their telescopes are diffraction limited, but they don't state over what field of view.
The spreading of the light in the Newtonian is mostly due to coma, but there is also some astigmatism. The corrector in the Lurie-Houghton eliminates the coma but leaves some astigmatism that is seen as spreading of the light bundle. Since the Newtonian uses only mirrors and no lenses it doesn't have any chromatic (color) aberrations. That's why the spot diagrams don't show any color effects. Note the scale change for the wider fields in the spot diagrams for the Newtonian. The coma is so bad that a large percentage of the light is far outside of the diffraction limit.
Spot Diagram 0.0417 Degrees Off-Axis (5 arc-min FOV)
Spot Diagram 0.3 Degrees Off-Axis (36 arc-min FOV)
Spot Diagram 0.6 Degrees Off-Axis (72 arc-min FOV)
The modulation transfer curves
This second set of diagrams are the Modulation Transfer (MTF) curves. They show how the image contrast is affected by aberrations in the optical system. Each of these graphs have a line that shows the upper limit or maximum contrast possible for a given telescope design. The limit is set by the aperture size and amount of central obstruction due to the secondary mirror.
Notice in the MTF curves that the Newtonian with a 5 arc-minute field of view has almost the same amount of contrast degradation as the Lurie-Houghton with a 72 arc-minute or 1.2 degree field of view. The Lurie-Houghton provides a field of view over 14 times wider with the same amount of contrast reduction! Also, the spot diagrams show that the star images away from the center of view will be sharper and brighter in the Lurie-Houghton, because the light is still concentrated within the diffraction limited airy disc.
Modulation Transfer Function 0.0417 Degrees Off-Axis (5 arc-min FOV)
Modulation Transfer Function 0.3 Degrees Off-Axis (36 arc-min FOV)
Modulation Transfer Function 0.6 Degrees Off-Axis (72 arc-min FOV)
How does the central obstruction affect the contrast?
The central obstruction that is normally present in reflecting type telescope is there because some type of mirror is needed to reflect the light from the primary mirror to the eyepiece. Because the mirror focuses the light back along its central axis, the secondary mirror must be on that axis, causing it to block the central portion of the light path. If the secondary mirror is no larger than 20 percent of the diameter of the telescope aperture, it causes virtually no degradation to the contrast of the image. Using OSLO LT, I compared the on-axis modulation transfer curve of my Lurie-Houghton telescope to an ideal lens with the same focal length and no central obstruction. I also analyzed different size ideal lenses of the same focal length as my Lurie-Houghton to find the ideal unobstructed telescope that gave the same contrast performance.
By performing this exercise, I was able to find the aperture of an ideal telescope, if such a thing could be built, that would give equivalent contrast on objects such as the planets. I did this because in the telescope world, there is the equivalent of a Macintosh vs. PC battle. In this case, the battle is between refracting (unobstructed) and reflecting (obstructed) telescopes. The refracting camp states that no amount of obstruction is tolerable. The results of my analysis, seen in the following figure, shows that an ideal (no aberrations) telescope with no obstruction and a 6.6" aperture would have the same contrast as my telescope for medium resolutions (ie. planetary observing). The graph also shows that the larger aperture with obstruction (in this case 31.6%) has much better contrast at higher resolutions. This is great for observing double stars and various star clusters where the stars are visually very close together.
People pay exuberant prices for excellent refractors with an aperture in this size range. Most reflectors cost much less per inch of aperture than refractors, so a reflecting telescope with more aperture and a reasonable amount of central obstruction can have the same or better planetary views along with much better resolution. A 9.8" telescope with a 3.1" central obstruction also has twice the light collecting area than the unobstructed 6.6" aperture, so it can show the observer objects that are half as bright. In terms of astronomical magnitudes (brightness scale), the larger telescope can see objects about 0.75 magnitudes dimmer with the same or better contrast and higher resolution for less money. Think about it, which would you buy?
How about some pretty pictures?
Here is a 3D rendering of the corrector lens cell with the two lenses in it.
I made this rendering in AutoCAD by making 3D solid models of the parts and
assigning colors or material properties to each of them. I removed a quarter
section to make the construction clearly visible. The side visible in this
drawing is the side facing the primary lens.
This rendering shows the front of the telescope with half of the tube removed
and no focuser. The secondary mirror assembly is attached through the center
hole of the first corrector lens.
Here is a 3D rendering of the corrector lens cell with the two lenses in it. I made this rendering in AutoCAD by making 3D solid models of the parts and assigning colors or material properties to each of them. I removed a quarter section to make the construction clearly visible. The side visible in this drawing is the side facing the primary lens.
This rendering shows the front of the telescope with half of the tube removed and no focuser. The secondary mirror assembly is attached through the center hole of the first corrector lens.
Updated: 24 February 2000