Feeds:
Posts

## The beautiful Sun

The above photo was captured during the evening of June 15, 2011 when I was waiting for the lunar eclipse. A Canon EOS 400D camera was attached to the Celestron Nexstar 4 inch Maksutov telescope in prime focus mode.

## Telescopes: basic parameters

It happens quite often to ask if a specific telescope can “show” a certain object with given magnitude. For this reason, it is useful to keep in mind a few simple relations giving the basic properties of telescopes.In this post, I explain three parameters: Limiting magnitude, resolving power, and the magnification.

Limiting magnitude is the magnitude of the faintest object one can see through a telescope. The larger the telescope aperture, the larger the light gathering power (w.r.t. the human eye), and the larger the limiting magnitude. It is given by the following relation:

Limiting Magnitude = 2.7 + 5 Log(D)

where D is the diameter of the telescope objective (lens or mirror) in mm. To have a more realistic estimate, you may subtract 0.5 from the given values. This is due to dirty optics and old coatings. For many small telescopes, you can see the numerical result in the below table.

Another important property of any telescope is its resolving power. The Rayleigh limit tells us if two stars are apart by an angle α, we can resolve them marginally if it satisfies the following relation:

α [arc second] = 1.22 λ [m] / D [m] * 206265.

where λ is the wavelength of observation, e.g., take 500 nm, and D is again the diameter of the objective.  Note that due to atmospheric turbulence, the resolving power is bound by atmospheric seeing. When seeing is good, i.e., the atmosphere is stable and has not too much turbulence, the resolution can be as low as one arc seconds. However, a typical value of 2-3 arc seconds is normal for many observing sites. Actually, this is one of the key parameters when professional astronomers try to find a good site for a new telescope. The reason the Hubble space telescope with a 2.4 m mirror captures sharpest ever images, way sharper than, e.g., 10m Keck telescopes, is due to atmospheric turbulence. For small amateur telescopes, the seeing effect can be traced with the amount of wobbling a bright star or planet shows in the eyepiece.

Magnification is defined as the ratio between the apparent angular size of an object in the telescope (through the eyepiece) , and its real angular size on the sky. It is calculated from the ratio between the objective focal length and the eyepiece focal length. In my opinion, one of the least important parameters in a telescope is its magnification. I put a rather conservative low to normal magnification, I personally use in the last column. Larger magnifications can be reached by using eyepiece with smaller focal length. However, again due to seeing effects, there is a practical limit, regardless of the size of the telescope, which is about 500x. When we use large magnification for faint or diffuse objects, not only focusing gets very hard, but also the surface brightness falls down. Hence, a large magnification is only recommended for planets and multiple stars.

I plan to discuss optical aberrations  of telescopes in a separate post.

## Why do I love CATs?

A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as search lights, headlamps, early lighthouse focusing systems, optical telescopes, microscopes, and telephoto lenses. Other optical systems that use lenses and mirrors are also referred to as “catadioptric” such as surveillance catadioptric sensors.

Catadioptric telescopes are optical telescopes that combine specifically shaped mirrors and lenses in designs that have all spherical surfaces that are easier to manufacture, have an overall greater degree of error correction than their all lens or mirror counterparts, have a wide field of view, take advantage of a folded optical path, or a combination of any or all of these attributes. Many types employ “correctors”, a lens or curved mirror in a combined image-forming optical system so that the reflective or refractive element can correct the aberrations produced by its counterpart.

Catadioptric dialytes are the earliest type of catadioptric telescope. They consist of a single element refractor objective combined with a silver backed negative lens (similar to a Mangin mirror). The first of these was the Hamiltonian telescope patented by W. F. Hamilton in 1814. The Schupmann medial telescope designed by German optician Ludwig Schupmann near the end of the 19th century placed the catadioptric mirror beyond the focus of the refractor primary and added a 3rd correcting/focusing lens to the system.

### Full aperture Correctors

There are several telescope designs that take advantage of placing full diameter lens (commonly called a “corrector plate“) in front of a spherical primary mirror. These designs take advantage of all the surfaces being “spherically symmetrical” and were originally invented to create optical systems with very fast focal ratios (wide fields of view) with little coma or astigmatism for use as astrographic cameras. They work by combining a spherical mirrors ability reflect light back to the same point with large lens at the front of the system (a corrector) that slightly bends the incoming light, allowing the spherical mirror to image objects at infinity.  Some of these designs have been adapted to create compact long focal length catadioptric cassegrains ( a cassegrain reflector is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes).

### The Schmidt corrector plate

The Schmidt corrector, the first full diameter corrector plate, was used in Bernhard Schmidt‘s 1931 Schmidt camera. The Schmidt camera is a wide field photographic telescope, with the corrector plate at the center of curvature of the primary mirror, producing an image at a focus inside the tube assembly where a curved film plate or detector is mounted. The relatively thin light weight corrector allows Schmidt cameras to be constructed in diameters up to 1.3 m. The corrector’s complex shape takes several processes to make, starting with a flat piece of optical glass, placing a vacuum on one side of it to curve the whole piece, then grinding and polishing the other side flat to achieve the exact shape required to correct the spherical aberration caused by the primary mirror. The design has lent its self to many Schmidt variants.

Popular sub-types
• Schmidt-Cassegrain telescopes are one of the most popular commercial designs on the amateur astronomical market, having been mass-produced since the 1960’s. The design replaces the Schmidt Camera film holder with a Cassegrain secondary mirror making a folded optical path with a long focal length and a narrow field of view.

### The meniscus corrector shell

The idea of replacing the complicated Schmidt corrector plate with an easy to manufacture full aperture spherical meniscus lens (a meniscus corrector shell) to create a wide field telescope occurred to at least 4 optical designers in early 1940’s war torn Europe, including Albert Bouwers (1940), Dmitri Dmitrievich Maksutov(1941), K. Penning, and Dennis Gabor (1941). War time secrecy kept these inventors from knowing about each others designs leading to each being an independent invention. Albert Bouwers built a prototype meniscus telescope in August of 1940 and patented it in February of 1941. It used a spherically concentric meniscus and was only suitable as a monochromatic astronomical camera. In a later design he added a cemented doublet to correct chromatic aberration. Dmitri Maksutov built a prototype for a similar type of meniscus telescope, the Maksutov telescope, in October of 1941 and patented in November of that same year. His design corrected spherical and chromatic aberrations by placing a slightly positive shaped meniscus corrector closer to the primary mirror.

Popular sub-types
• Maksutov Cassegrain telescopes are the most commonly seen design that uses a meniscus corrector, a variant of the Maksutov telescope. It has a silvered “spot” secondary on the corrector making a long focal length but compact (folded optical path) telescope with a narrow field of view. This design idea appeared in Dmitri Maksutov’s 1941 notes and was original developed in commercial designs by Lawrence Braymer (Questar, 1954), and John Gregory (1955 patent). The combination of the corrector with the silvered secondary spot makes Maksutov Cassegrains low maintenance and ruggedized since they can be air sealed and fixed in alignment (collimation).

### Schmidt-Cassegrain or Maksutov-Cassegrain?

The SC cools more quicker, and thus you get better images sooner than the very thick corrector of a Mak/Cass. The Maks are also heavier than SC, as my 8″ Mak needs a mount that would hold an 11″ SC.

All told, they both hold alignment fairly well, and the optics are kept cleaner due to sealed OTA.

The Mak/Cass should give better images but I find it difficult to tell the difference between 8″ scopes of these two types. I hear people say when they look through mine, that subtle planetary details are a bit more apparent.

The Mak is certainly more expensive inch for inch compared to an SC. They are also fairly uncommon.

Since all the optics in an MCT are spherical (the primary, the secondary, and both sides of the corrector), and since making and testing spherical optics is easier, it takes less work to shape and polish MCT optics to a higher precision. In comparison, SCT corrector plates, with their weird curve, are difficult to shape correctly and next to impossible to polish to maximum smoothness. So it’s not really that the MCT design gives superior images, it’s just that MCT optics tend to be of higher overall quality than an SCT of the same size.

Most MCT’s have a proportionally longer tube than a comparable SCT owing to the longer focal ratio of the primary mirror. Thus in the larger sizes, an MCT will end up being bulkier, and it will be more expensive (due to the cost of the corrector, mentioned previously). Also, due largely to the thickness of the meniscus corrector, the time required for an MCT to adjust itself  to the outdoor temperature will be greater than for an SCT. In the plus column is the fact that the image sharpness in a well-made MCT is generally better than in any SCT.