# How does a cross dispersed spectrum look like in a reality (from echelle spectrographs)?

I am an analytical chemist with some interest in amateur spectroscopy. Since astronomers use echelle spectrographs to study the high resolution spectrum of the stars, someone suggested to post the query here. An echelle grating produces a spectrum with several overlapping orders. One can then use a cross-disperser, which could be a prism or a grating, which can separate the overlapping orders and then we obtain a very high resolution spectrum. I want to know how a real echelle spectrogram looks like -as if we were looking at the 2D spectrum with our naked eyes?

I have a small echelle grating (79 grooves/mm, 75$$^o$$ blaze) and tried to visually generate a 2D spectrum with the help of a plastic transmission grating. The light source was an ordinary fluorescent lamp Pictures are posted below. The experiment is too elementary. A horizontal slit made by two blades as an entrance on the shorter rectangle of a shoebox. The light from the slit falls on the reflective echelle. On the larger side of the shoebox, I made a window to take a picture.

Picture 1: A vertical slit made in a cardboard box, the long side of the echelle is perpendicular to slit An expected overlapping order spectrum seen.

Picture 2: A horizontal slit made in the cardboard box, now the long side of the echelle is parallel to the slit

Now, if we hold a plastic transmission grating (Edmund) in our hand, with its rulings perpendicular to the echelle, and view the echelle through that transmission grating, I can photograph the following 2D spectrum.

Picture 3: Hold a transmission grating with its rulings crossed with the echelle and view picture no. 2.

Unfortunately, this looks like a replica of a spectrum rather than separation of orders.

**The main question: How should one hold the transmission grating in order to visually see the separated orders. Picture no. 3, was supposedly, separation of orders but it does not look like it.

If this were a true 2D spectrum we should see some increasing distance between Hg green lines. All separated orders look the same resolution. Is there any other simple way to see a true cross dispersed spectrum with eyes using a simple cardboard type box? The key problem seems to be the issue how should we hold the transmission grating in order to see a true 2D spectrum unlike Picture 3.**

EDIT

After Prof.ELNJ's suggestion in the answer, I wanted to confirm if this is what he meant. The grating has an arrow with a pencil (from ThorLabs) which shows the blaze direction because by viewing in this direction one can see a "rainbow" of colors. So the arrow is towards the viewer, and I hold a transmission grating "crossed" with the echelle ruling.

Rough view of what appears to the eye

• I don't understand your question. You have a picture of a real echellogram. That is what it looks like; when you get the optics right. Did you put a dekker on the slit? Echelle spectrographs cannot use a "long slit". – Rob Jeffries Aug 9 at 0:28
• You are talking about the grey scale figure? Is this it would look like if we could "use" our eyes at the exit of an echelle spectrograph? I am adding more pictures to show how a vertical slit looks like? The slits are nothing but a two blades horizontal as well as vertical at the entrance of a cardboard box. – M. Farooq Aug 9 at 0:37
• @M.Farooq it would be good to refine this a little more and make sure there's a specific Astronomy-related question that can have a specific Astronomy-related answer and is clearly indicated. There's a lot here and its hard to tell exactly which part to answer. As pointed out the B&W image does indicate (without color) what it would look like if we could see it. Of course they are usually too dim to see, but if the light were bright enough to be detectable but not bright enough for our color perception to kick-in, then if you put a piece of paper at the focal plane it might look like that. – uhoh Aug 9 at 1:55
• I think this should be broken up into several questions and some parts might be better in Physics SE, especially about how exactly to do the cross-dispersion for a DIY echelle spectrograph. I think asking for how to find early, historical echelle photoplate images or spectrograph designs might be instructive since the early ones will show many of the effects that were designed out by later, more complex instruments and then CCDs. – uhoh Aug 9 at 1:59
• I really can't understand what your pictures are. Picture 1 looks as I expect - overlapping orders. What is picture 2? Picture 3 appears to show multiple, vertical copies of the same spectrum - I cannot see how you get this from picture 1. The last picture is a CCD image of an echelle spectrum – Rob Jeffries Aug 9 at 8:32

You are doing it incorrectly if you are trying to cross-disperse your Fig.2. You should be cross-dispersing your Fig.1.

A "cross-dispersed" spectrum requires requires the dispersive elements to be at right angles.

Your Fig.1 shows the dispersed spectrum from the echelle with overlapping orders.

To separate the orders you view Fig.1 with the cross-dispersing element, but with the cross-disperser dispersion direction placed along the y-axis of your pictures. A schematic would be something like this, where the grating rulings are indicated with lines. (I believe this picture is originally from Optical Astronomical Spectroscopy, by C. R. Kitchin).

The slit orientation would be parallel to the rulings on the echelle, but you need to make the slit short enough that the orders can be separated by the cross-disperser.

That should produce something like that shown below, if you illuminate it with a continuum source. Exactly what you see will depend on the dispersive power of the cross-disperser (should be low and often, prisms are used), how large your CCD is and how long your slit is.

• Comments are not for extended discussion; this conversation has been moved to chat. – called2voyage Aug 10 at 14:11

Visualizing a cross-dispersed echelle spectrum directly is a nice experiment to do (I do it with my upper-level astronomy students when I teach about this) but it's a little tricky because your intuition from other types of gratings can lead you astray in terms of how to arrange things for viewing.

The key is to realize that the blaze angle of an echelle grating is very high, often 60° or more. (I see yours is 75°.) Here's a diagram that helps to visualize the implications of this:

(from here)

If you look at the light path for the echelle grating there, you can see that it is illuminated at a very steep angle, and that the dispersed light goes nearly back in the same direction as the illumination. That tells you what you need to do, namely to have a light source that is coming from next to (or even behind) your head, so that the light is shining toward the grating more or less in the same direction you are looking. You want the light to be incident on the grating at something close to perpendicular to the tilted faces of the facets.

Here's what I do:

1. Place your echelle grating on a flat surface like a table, oriented so that the short side of the rectangle is facing you.
2. For a light source, I use a small LED flashlight, and cut out a piece of cardboard to mask most of the output, only letting through a small circle of light (like just one of the LEDs).
3. In one hand, hold the flashlight next to your face, pointing toward the grating.
4. In the other hand, you can hold a regular transmission grating to use as your cross-disperser. Look through the handheld grating at the echelle grating as you illuminate it with the flashlight. You may need to experiment to see which way to turn your grating in order to have its dispersion perpendicular to that from the echelle.
5. Depending on the blaze angle, you may need to crouch down so that you are looking at the echelle grating at a low enough angle. With your 75° blaze angle, that means you want to illuminate and view the grating only about 15° from horizontal. Again, referring to the picture above will help you see what to do.

Edit: It also helps to darken the room as much as possible so that the light you’re seeing is (as much as possible) just from that one beam, without stray light coming in from other angles.

Good luck! Feel free to follow up with questions.

• Thanks this is exactly what I was asking in what is the trick to see a true 2D echellogram. I have added a picture which shows that the blaze is towards me and I hold a grating crossed with this echelle. Is this the arrangement you suggest when you show it to students. I have added a picture for confirmation. – M. Farooq Aug 15 at 16:48
• Yes, that’s correct. You may need to rotate the handheld grating by 90 degrees - just try it and see. With one orientation you should see a narrow white-ish band (because of the overlapping orders) and in the other orientation you’ll see them offset from each other vertically. Now you just need a dark room and a bright, narrow light source. I’ll edit my answer to clarify that a dark room helps. – ELNJ Aug 15 at 18:16
• One more question, if we were to make a rectangular slit on a LED, will the slit long side be parallel to echelle ruling? – M. Farooq Aug 15 at 19:09
• Yes, I think that’s right. The dispersion should be perpendicular to the rulings, so it’s ok to have your light source extended parallel to the rulings. The only limitation is that you need enough dispersion in your cross disperser to separate the orders. The longer your slit, the taller each order will be, and the more cross-dispersion you need to separate them. – ELNJ Aug 15 at 19:55
• Okay, thanks, makes sense. The way I am holding the plastic one makes the transmission grating's ruling perpendicular to the echelle grating. If I rotate it by 90, the rulings of both gratings are parallel. I think your students are lucky if you teach this to them. Textbook figures do not give clue of the orientations and that has perplexed for 5-6 years. – M. Farooq Aug 15 at 20:05