Lecture 10: Telescopes -- for UV, Visible, and Infrared
At visible wavelengths two principal types of telescopes can be used:
Refractor: designed around a lens that uses the bending of light in glass (refraction) to form an image of a distant object:
Refractors are based on the fact that light's path is bent when making a transition from one medium to another.
Reflector: designed around a curved mirror that forms an image of a object (as discussed later, this type of telescope can be designed to operate over a much broader range of wavelengths than a refractor). The curve on a reflector is usually a parabola.
For infrared (IR) and ultraviolet (UV) observing, reflectors are greatly preferred because most lens materials (eg. glass) are not transparent at these wavelengths. A reflecting telescope can work from the UV throght visible wavlengths and into the IR.
Measures of Telescope Performance
Magnification is often quoted for small telescopes but is not a fundamental property of a telescope but rather of how the image from the telescope is viewed. High magnification cannot compensate for poor resolving power.
D = telescope diameter
Light gathering power is equal to the area of the telescope's objective (front lens or primary mirror)
So ability to detect a faint source improves as the square of the telescope diameter -- the U of A's project to upgrade the Multiple Mirror telescope from the equivalent of 4.5-meters to 6.5 meters has lead to improved light gathering power of
The finest detail (or equivalently the smallest angular size that can be measured) is controlled by diffraction in a perfect telescope. The telescope acts a circular aperture that collects the starlight with diffraction occurring because the telescope is finite in diameter. By considering the interference of light waves hitting the telescope at different points across the mouth of the telescope, the following relation can be derived:
Note that the full description of the image of a point source at the focal plane of a telescope is
Here's a plot of the intensity (which makes the connection between diffraction and interference obvious with this alternating pattern of light and dark) :
Note that the equation for resolving power above gives the diameter of the first dark ring. This behavior of diffraction of light passing through a telescope explains why the images of stars produced by a camera on the Hubble Telescope look the way they do:
(the diagonal lines and squarish character of the diffraction rings are due to the vanes holding the secondary mirror of the telescope and the square sampling of the image due to the detector being used).
Example: We want to study a planet orbiting a star. This system has an apparent separation of 2". We want to observe at a wavelength of 1900 nm because of an interesting spectral line due to water. How large a telescope must we use to see the star and planet separately?
Telescope Plate Scale
Another useful parameter in analyzing a telescope's performance is its plate scale -- the relation between an angular distance on the sky and a physical distance in the telescope's focal plane where you place an instrument to detect the telescope's output:
Example: Steward has a 2.3-meter telescope used at f/45. What is the plate scale in "/mm?
D=2.3 meter f/=45 plate scale =1/(45*2.3) = .00966 radians/meter
.00966 radians/meter = .00966 radians * 206265 "/radian * 1/1000mm/meter = 2.0 "/mm
[short-cut formula: "/mm = 206265"/(f/*D*1000) ]
Practical Considerations in Building Telescopes
Refracting telescopes are rarely built anymore because
1) Lenses have significant refracting power only over a limited range of wavelengths and may even be opaque for most wavelengths.
2) Even for wavelengths where lenses are effective, the fact that a lens can only be supported around its edge which limits the performance of the lens due to effects such as sagging under the influence of gravity.
Consequently all modern telescopes are reflectors.
Influence of the Atmosphere on Observations
The atmosphere is opaque over most of the electromagnetic spectrum with only visible, part of the infrared, part of the microwave, and the radio portions of the spectrum useable from the ground -- this is one the prime motivations for building space telescopes.
The other impact of the atmosphere is the degradation of angular resolution due to pockets of varying density of air (and also due to motions of these air pockets) along the line of sight to a star. This "seeing" causes a star image to shimmer, move, and to have an angular diameter usually much larger than the diffraction limit of the telescope. Typical seeing causes star images to have a diameter of ~1" at visible wavelengths.
Adaptive optics refers to schemes to measure the refractive properties of the atmosphere and remove seeing by use of a deformable mirror within a telescope to compensate for seeing. Because such schemes cannot work well over a large field-of-view, another reason for building space telescopes is to avoid seeing.
Detection of Electromagnetic Radiation
Techniques varying with wavelength range:
Gamma-rays, x-rays can be detected with photographic plates, but electronic detectors which can count individual photons are preferred.
Ultraviolet and visible light is now usually detected with CCDs (charge coupled devices).
Infrared through about 40µm uses composite detectors which are similar to CCDs in many respects.
Some common principles behind electronic imaging:
Pixels: A scene is focussed onto the surface of a semiconductor which is sensitive to light. This surface will be subdivided into units each of which an make an independent measurement of the amount of light falling on it. These units are called pixels. If the detector has enough pixels, the subdividing of the image into these units is hardly noticeable.
Electronic detectors have two main parts:
The light sensitive layers absorb photons which release electrons in proportion to the number of incident photons (hence these detectors are called "linear"). Electronic detectors absorb and record a much larger fraction of the photons hitting them than do photographic plates.
Uncertainties in Using Electronic Detectors
Whenever an experiment is done where objects are counted, a natural uncertainty arises. Other types of errors or uncertainty may also be present --for example, the night sky is not completely dark so that the photons from a very faint source may be so small compared to the photons from the sky as to be unnoticeable.
In the case of counting photons, if N photons are counted, there is an uncertainty equal to N½ in the number counted. This means that if you imaged a star and took a large number of exposures, the number of photons would not always equal N but would average to N with a spread in values of N½.. If you took only one exposure, you could say how many photons you received but you should be cognizant of the fact that the "true" value could be different by as much as N½.
For example, you measure a star and get 1300 photons. You need to state that your measurement is likely to be uncertain by (1300)½= 36.06 or nearly 3%. There is no way to avoid this -- you can make it less troublesome by repeating exposures many times to insure that you have the average measured correctly!