Telescope Desiderata

Various Goals Imagery / surveys - discovery, census – Consider scales, POSS vs HST, etc Astrometry / motions / distances Photometry (in various bandpasses) –why? Spectroscopy: – compositions, velocities, rotations, mag fields etc

What would we want from an Ideal Telescope? Large collecting area Low-mass (why?) Stable figure (esp thermal sensitivity and mechanical loading) High optical quality (ideal surfaces) Large image scale (why?) Large field of view Flat image plane

Yet more… No chromatic aberrations No optical aberrations (coma, astigmatism) Minimal refracting elements Minimal reflecting surfaces, optimally coated Multiple focal positions / f-ratios / scales Stability in tracking and pointing Variable tracking rates (why?) Global coverage of whole sky? (from what locations on Earth? Why?)

Image scale What determines the scale we want? - theoretical resolution limit? - detector pixels (what sampling?) - seeing? Q: how will we be doing our science? For example, stellar photometry in crowded fields?

Stellar photometry?

A sample study Consider a direct image taken at the prime focus of the CFHT, using the Megacam instrument (say).

Some Numbers: The CFHT has a primary mirror m in diameter. Its f/ratio at prime is 4.18, which means that the focal length L is 4.18 x = metres For image scale, remember θ = d / L (in radians, if d and L are in the same units). Thus d, the size of the image on the detector, is given by L θ Remember that 1 radian = arcsec So a star-like object subtending 1 arcsec on the sky (typical “seeing”) has a linear size d on the detector of (15.01) x (1 / ) metres = metres

Continuing: metres = 73 microns = the “size” of the star’s seeing disk Megacam’s CCDs have pixels (detecting elements) that are 15 microns on a side. This means that each star image is ‘splashed over’ a square that is bigger than 5 x 5 pixels in size (Remember that the seeing is “FWHM” – there is light and energy in the broader wings too!). Is this useful, or wasteful? Why not use bigger pixels (or a different focal length) to make each star fit into just one pixel?

In Other Words: Is This Wasteful? (Among other things, CCDs have finite sizes! Do we need to dedicate so much area to each star?)

Consider Stars in Close Proximity Can we separate them? – measure the brightness of each, deal with crowded fields, etc? THAT is the point of having images spread over a well-sampled image plane, thereby allowing us to disentangle separate sources. (PSF-fitting photometry!)

Forget Atmospheric Degradation If you can reach the theoretical limit, what do star images look like? How can you tell when one ‘blob’ of light is actually adjacent two point- like sources? Answer: the intensity distribution in the image plane is given by the 2D-Fourier transform of the illuminated aperture (remarkably!)

e.g. for a square mirror:

More realistic: an annulus

In the Limit With a perfect mirror and no “seeing”, star images will be ‘Airy’ profiles.

When are Stars ‘Resolved’? Rayleigh limit: the peak of one star lies on the first null in the Airy profile of the other.

But Traditionally Excellent “seeing” was understood to be about 1 arcsec The Rayleigh criterion is given by θ (radians) = 1.22 λ / D In visible light, λ= 500 nm = 5 x metres So for θ = 1 arcsec = 1/ rad, D = 1.22 x (5 x ) x = m = 13 cm In other words, telescopes bigger than this will not attain the diffraction limit: the ‘natural seeing’ blurs our view.

But We Can Beat This! Use ‘adaptive optics.’ Watch Did we actually need to build the Hubble Space Telescope?

One AO Result Watch

Resolution at Other Wavelengths (esp radio, even in the absence of “seeing”!) The solution? ‘Dilute’ apertures

Back to Observatories: Where, how and why? Sea level, at altitude, in space? Where on Earth? If in space, in what orbits?

How About the Detectors? High quantum efficiency (record all the photons!) Panchromatic response (filters)? Fine-grain (high resolution) Large detecting area Linearity Large dynamic range Readout: quick, lossless, non-destructive Short time constant (no latency) Digital output if possible Minimal background noise (plate fog, read noise, thermal IR, cosmic rays) Ease of operation, preferably remotely

How about the Instruments? Simple optical paths Remotely operable Tolerable data rates Standardized outputs Filter and shutter mechanisms, coronagraphs, etc Minimize scattered light, ghost images Real-time display /monitoring / IQE Archivable Pre-processed (‘take out the instrument’) Multi-purpose vs dedicated? Multiplex capabilities Parallel (serendipitous) functions Polarimetric

Other Issues Compensating for periodic tracking errors, tip-tilt, seeing. Guide-star mechanisms. Atmospheric dispersion, refraction, effective wavelength. Active vs adaptive optics; multi-conjugate correction. The need for guide stars; lasers. Absolute calibration issues

Other Wavelengths What are the Fundamental Constraints? From long to short: – Radio – Infrared – (optical) – UV – X-ray – Gamma-ray

Measures of Quality “Seeing” - FWHM? Or some other? Where is all the power? Strehl ratio Wavefront errors

Telescope Designs Refracting Reflecting Some combination – Consider Schmidts, catadioptrics, etc What mirror figures? Spherical? Paraboloidal? Hyperboloidal? Ellipsoidal? How many mirrors?

Optical Telescope Configurations Prime; Newtonian; Cassegrain; Gregorian; Coude; Naysmith Mountings Zenith Transit Equatorial (pro and con) Alt-az (complications!)

Aberrations (and their solutions) Chromatic Spherical (consider Schmidt telescopes!) Coma (consider paraboloids) Astigmatism Field curvature Distortion Vignetting

Attributes Focal length – long creates large image scale f-ratio (‘fast’ or ‘slow’) - affects sensitivity to different surface brightnesses Field of view