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

Question

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

Answer 1

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.

Answer 2

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.