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Astronomical Techniques ILecture 12

Yogesh Wadadekar

Jan-Feb 2015

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Objective prism imagers: place prism over telescopeprimary

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Principle of diffraction gratings

Maxima in the output intensity occur at a sequence of anglessin θn = nλ/d .

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Diffraction grating contains many slits. Order 1onwards, separation happens!

gratings contain hundreds to thousands of grooves/mm.IUCAA-NCRA Grad School 4 / 27

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proof of grating equation with reflection grating

nλ = d(sinα+ sinβn)

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reflection grating

Sign convention: α and β have opposite signs if they are on oppositesides of the grating normal.

for m = 0 grating acts as a mirror α = −βfor m > 0, β > −αfor m < 0 β < −α

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Blazed grating -Littrow configuration

2d sin θB = mλ

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Reflection and transmission gratings

How is this transmission grating different from a prism?

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Pattern for many slits - monochromatic light

The addition of slits increases the sharpness and brightness of thepeaks but leaves the locations of the orders unchanged. Of course,slight peak offset for slightly differing wavelength.

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But different orders overlap!

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Resolution of grating

If grating is illuminated by polychromatic light. In a given order, redderlight is diffracted to larger angles than blue light. The maxima foradjacent wavelengths in a given order are offset slightly. Spectralresolution for order n is determined by the wavelength shift needed toplace the diffraction pattern maximum for λ+ δλ on the first minimumin the pattern for λ. The resolution is:

< =λ

δλ= nN

so it depends both on the order and on the total number of slitsilluminated on the grating N.

IUCAA-NCRA Grad School 11 / 27

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Angular dispersion

in order n is given by:dθdλ

=n

d cos θHigher dispersion corresponds to larger values of this quantity.Echelles take advantage of both n and θ dependence to maximizedispersion.

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Astronomers working definition of dispersion

Astronomers often use the word dispersion to refer to dλ/dx in thespectrograph focal plane, usually quoted in Å per mm. This is moreproperly called the “linear reciprocal dispersion”. It is inversely relatedto the angular dispersion, so lower values correspond to higherwavelength dispersion. e.g. Sloan Survey has 3 Å per pixel (24 µm).

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Advantages of gratings

Dispersion same for all wavelengths in given orderLarge dispersions/resolutions possible (large n)Transmission or reflection gratings availableHigh UV throughputs possible (with proper reflection coating)Grating technology highly developed, extensive customizationpossible

IUCAA-NCRA Grad School 14 / 27

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Disadvantages of gratings

Size limited by capacity of ruling engine. Use of mosaic gratingswith large beam telescopes possible but performancecompromised.Order superposition: red light of a given order is spatiallycoincident with blue light from a higher order. In echellespectrographs, use a second grating as a cross-disperser.Low efficiency: Gratings distribute light across a large number oforders (including the zeroth order, which has no dispersion). Fluxdecreases rapidly with order. Solution: Blazed reflection gratings,in which the facets of the slits are cut at an angle that places themaximum of the single-aperture pattern at a chosen wavelengthand order.

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Echelle grating and cross disperser

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How gratings are manufactured

a master is prepared with a diamond tool making closely spacedgrooves on metal - high cost.many replicas can be made with plastic using the metal grating asmaster.these can be mounted on glass to form a transmission grating orcoated with a reflective material to form reflection grating.

IUCAA-NCRA Grad School 17 / 27

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Grism - Prism + Diffraction grating

A grism is a combination of a prism and grating arranged to keep lightat a chosen central wavelength undeviated as it passes through acamera.

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Spectrograph variants: Double spectrographs

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Spectrograph variants: Fiber fed multi-objectspectrographs (1D)

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SDSS plugplate

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Long slit spectroscopy (2D)

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Long slit spectroscopy

Which way is the galaxy rotating?

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All detector imaging steps apply for spectroscopy

Bias subtraction, Dark subtraction, flat fielding, cosmic ray removal,bad pixel interpolation etc. are required for spectroscopic data.

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Integral field spectrograph (3D)

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Tiling a galaxy with lenslets

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Integral field spectrograph

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