Cryogenic Materials

Cryogenic lens designers of large optics need to know what materials are available and in what size. As of 19-Sept-2019 I’ve identified the following materials:

Up to 200 mm in diameter with good (> 90% in 10 mm samples) throughput up to 2.45 µm in wavelength are:

  • ZnSe
  • E-SF03
  • Calcium Fluoride (CaF2)
  • Infrasil (Heraeus fused silica)
  • BaF2
  • S-FTM16
  • S-PHM52
  • S-TIM28
  • S-TIM1

Up to 100 mm in diameter include:

  • S-NPH2
  • S-TIH14
  • S-TIH1

Those interested can grab glass catalogs from my drive. Note, these catalogs do not contain the cryogenic index of refractions. Feel free to contact me with any questions or comments.

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Infrared Camera Design

Cryogenic (SWIR; 0.7 – 2.5 µm) infrared cameras are specialized. For astronomical purposes thermal radiation from a room-temperature lens would swamp the signal beyond 1.5 µm. To deal with this signal such cameras at low temperatures (say 120 Kelvin). The set of materials that is transmissive to 2.5 µm with *well known* indices of refraction at 120 K is quite small.

Thus, as a starting point for camera designers I provide an example lens. This all-spherical lens has an accessible (real) entrance pupil that is 150-mm in front of the first element. This 177-mm f/1.33 camera only uses CaF2, ZnSe and S-TIH1 (first negative element) yet achieve spots that are better than 5.4 µm in RMS radius! It drives a 2048 x 2048 x 18 µm pixel detector (with a 52-mm-diameter full field).

201906041735.jpg

Please let me know if this design helps get you started.

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R2S2I

Recently, with the help of postdoc Decker French we have been looking into the design of a new rapid-response spectrograph and imager. We lovingly call it R2S2I or the “Rapid Response Swope Spectrograph and Imager”.

The goal of R2S2I is to be the instrument of choice for rapid followup of transient events. The instrument has been designed as a followup based on lessons learned from both SED Machine (on the Palomar 60 inch) and FLOYDS (on the Las Cumbres Observatory 2 m).

R2S2I uses a wide-field and rapid-readout imager plus a slicer-based integral field unit. By using a slicer we’ll be able to classify thousands of transients per year down to r~20 on the 40-inch Henrietta Swope Telescope at Las Campanas Observatory. The spectrograph operates at a spectral resolution of 1,000: allowing to to both classify and perform some of the initial science.

201904241646.jpg

As a result R2S2I will be able to participate in this golden age of rapid-response astronomy. In just a few years a whole slew of facilities including LSST, ASAS-SN, ZTF, TESS, etc. will revolution time-domain astrophysics with alerts issued on tens-of-seconds timescales.

201904241647.jpg

Our long-term vision is to build not just one R2S2I but multiple. These could be fed by a small network of 1-m telescopes to play an important role in the long-term future of spectroscopic classification of transient events.

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Spectrograph 0th-Order Calculations

I’m trying to make a tool that allows the user to compute anything they ever wanted to know about spectrographs. It’s here:

DESIGN YOUR OWN SPECTROGRAPH: http://nickkonidaris.github.io/SpectrographCalculator/

The default parameters are for DBSP on the Hale 200-inch telescope. The parameters are listed the following format:

Parameter name (variable name) [ text box with value ]

If you put your mouse over a parameter name, you’ll see how the value is computed. The page displays the actual code to compute the variable. I know, documentation is needed.

Some notes:

1) The final variable called “pixel system throughput” (PST) allows you to compute the watt per pixel expected. Given a spectral irradiance from the source in erg / s / cm2 / Ang multiply by PST and you’re good to go.

2) If you’re worried about echelle spectrographs, set the grating rotation (grotate) to 0.

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Classical and β Anamorphism in Spectrographs

The anamorphic magnification of ruled-grating spectrographs is a property that must be understood and accounted for when designing ground-based spectrographs. Anamorphism is a general property of geometric optical systems with. Specific to spectrographs, anamorphic magnification is a scalar value defined as the ratio of diameters of the major to minor axis in the pupil. Anamorphism arises when a grating is used off of the Littrow condition.

In this post I show “classical” anamorphism that arises from tilting a grating around its rulings, as well as rotation or \beta anamorphism that arises from rotating a grating (see figures below for axis). I conclude by describing some key differences between tilt and \beta anamorphism.

Basic Theory

Classical anamorphism arises when a grating is tilted around its rulings. Based on the grating equation

cos \beta \cdot\left(sin\ \theta_{in} + sin\ \theta_{out}\right) = \frac{m \lambda}{d}

it is straightforward to compute the anamorphic factor as

r = \frac{cos\ \theta_{in}}{cos\ \theta_{out}}

The grating produces an elliptical shaped pupil with a minor axis diameter equal to the spectrograph beam size ø, and the major axis diameter is the anamorphic factor times the beam size (r \times \oslash). Note that if the spectrograph is operated in Littrow (e.g., high-resolution echelon spectrographs) then \theta_{in} = \theta_{out} and r is unity. If one uses grisms or volume-phase holographic gratings, the anamorphic factor again is unity. Reflective grating spectrographs often have anamorphic factors in the 1.3 to 1.5 range (see also Schweizer (1979)).

Classical tilt Anamorphism

To the observer, the main consequence of anamorphic magnification is a change in the plate scale of the spectrograph in the dispersion direction. Recall that the plate scale of a spectrograph is the (Telescope Diameter) ⨉ (Camera f/#) / 206265. For instance, the 10 m Keck telescope with an f/2.0 camera has a plate scale of 97.0 µm / arcsecond. With an anamorphic factor of 1.3, the plate scale is (Telescope Diameter) \times (Camera f/#) / (206265 \times r) or 75.0 µm /arcsecond. In short, the slit image shrunk in the dispersion direction.

To illustrate the point, I’ve used zemax raytraces to create a number of videos that demonstrate the phenomenon and effect of anamorphism. As the web page loads, the videos should play in sync (if not, try reloading). The optical model shown in these videos represents a simplified spectrograph.

In the spectrograph, a single circular collimated beam illuminates a grating. The grating is either tilted or rotated (which varies with each frame of the movie), and the outgoing beam is fed into a perfect (paraxial) camera. The grating operates at a wavelength of 550 nm, with a ruling density of 280 line per millimeter operating in fifth order. The movie begins in the Littrow configuration (\theta_{in} = \theta_{out} = 23\ degree and r = 1.0) and each frame of the movie increases the amount of grating tilt. As the tilt increases, the anamorphic factor increases to about 1.9.

The first frame shows the layout and ray traces. As the grating is tilted, the pupil on the camera increases in the dispersion direction. It is possible to measure the size of the beams on the screen with a ruler and compute the anamorphic factors.

The second video shows a footprint diagram of the beam on the camera. The footprint diagram shows a grid for reference, a black circle tracing the camera mouth, and an ellipse expanding outward showing the rim of rays on the camera. You’ll notice some numbers on the bottom that compute the radius of the beam. The anamorphic factor can be computed by taking the Ray Max Radius and dividing it by 150. You’ll note that the final frame has a max radius of ~290 mm so the final anamorphic factor computed from this diagram is 1.933. Note the dispersion direction is perfectly aligned with the axis of pupil elongation.

The third video shows an image on the detector. The image is comprised of dots where an individual ray hits the detector. The object is a series of horizontal lines, the envelope of the object is square. As the grating is tilted, the image of the object shrinks in the vertical direction (dispersion direction). The anamorphic advantage is that light from the object is concentrated into a smaller area as the anamorphic factor increases.

So we see here the pros and cons of tilt anamorphism. The anamorphic beam concentrates light from the object into fewer pixels, increasing the grasp of the instrument and decreasing the time to background limit. On the other hand, the beam presentation onto the camera is non circular and requires a larger and optically faster camera design.

Grating tilt anamorphsim - layout

Grating tilt anamorphism - footprint

Grating tilt anamorphism - spots

β-angle rotation anamorphism

The \beta angle is the angle projected along the line rulings in the grating. The effect of \beta is described in the grating equation from above. How \beta changes the pupil presentation and anamorphic factor is interesting and explored in this section.

In the previous section, I used zemax to raytrace beams through a simple spectrograph in order to observe the effect of tilting the grating in \theta_{in} from -23 degree to -60 degree. In this section I raytrace through the same spectrograph, but now rotate \beta from 0 degree to 45 degree.

The three figures in this section are similar to those in the previous. The main difference is that the layout is rotated by 90 degree in order to see the effect of \beta angle rotations. I won’t otherwise describe the figures again.

The result of \beta angle rotations is surprising. Look at the footprint diagram. Recall that the vertical direction is the dispersion direction, notice that the footprint in the vertical direction does not change size. As a result, the length of the dispersed spectrum doesn’t shrink. Take a look at the static footprint diagram where \beta is 45 degree. I have highlighted certain key features.

Now look at the movies. You’ll notice that pupil elongation angle is vertical for \beta \sim 0 and ends at almost 50 degree or so when \beta is 45 degree. As the \beta angle increases, the pupil in the spectral direction shrinks, while the pupil in the spatial direction stays the same. As a result, more pixels are required to capture the same spectrum in the spectral direction.

Grating rotation anamorphsim - layout

Grating rotation anamorphism - footprint

Grating rotation anamorphism - spots

Conclusions

  • Tilting the grating increases the tilt anamorphic factor in the dispersion direction. As anamorphism increases, the image shrinks in size, and the camera becomes harder to design than the no anamorphism case.

  • Rotating the grating increases the \beta anamorphic factor in a direction that is \sim45 degree from the dispersion direction. Unlike tilt anamorphism, \beta anamorphism increases the image size, and the camera becomes harder to design than the no anamorphism case.

  • The tilt anamorphic factor is inadequate for \beta anamorphism. A complete description of \beta anamorphism requires the pupil size and rotation angle are specified.

Bibliography

  • Schweizer, F. 1979, PASP, 91, 149
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New code repository

I’ve started a new github repository for the SED Machine control. The code is a series of python servers that communicate via XML RPC. A second “Konidaris python” repository was created. The KPY repository includes tools for atmospheric absorption, mirror reflectivity, centroids, function fitting, SED Machine, and zemax-python bridge via PyZDDE.

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Chimera 2 first light

Chimera 2, a new high-speed and wide-field imager for Palomar achieved first light! Gregg Hallinan is the PI, I’m proud to have performed the lens-design for this instrument, all optics are off-the-shelf, so the real challenge was the imaginative way in which the off-the-shelf optics were combined.

An example Chimera 2 first light image is shown below:

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