Rob, this is what I have been trying with a transmission grating...without success. From Picture 1, the expected overlapping spectrum, if I hold a transmission grating "crossed"...and view this, it does not work. If we look at picture #2, and then you see this picture no.3 which is not a true 2D spectrum. Certainly this simple demo does not seem to work.

What would be the y-axis? Perpendicular to the ruling direction?

One example DIY, astrosurf.com/buil/echelle/first.htm

Rob, I guess I was not clear. Picture no. 3 is the set up of picture no. 2 viewed by holding the transmission grating with its rulings crossed to the echelle. Imagine that transmission grating is in your hands and you are viewing picture no. 2 with it in a crossed position.

In short, picture no. 2 is producing picture no. 3.

@M.Farooq that is what I understood, and it not the way a cross-dispersed echelle works. Please read my answer.

@M.Farooq two thoughts; First, can you mention the lines per mm for both the echelle and the transmission grating and the blaze angle for the echelle? If your response is "What's a blaze angle?" then it's time to do some more reading. Perhaps you aren't using the echelle grating in the proper configuration yet. Second it might go a long way if you included a photo of your actual setup, no matter how DIY it looks?

The blaze angle is given in the question. There is no problem with the echelle grating illumination, as the first picture shows. @uhoh

@RobJeffries Yep I see the numbers now, we can wait for confirmation that the grating was actually tilted roughly 75° away from normal incidence. But now I'm concerned about the slit orientation shown in the first two Pictures. Picture 1 is probably the correct orientation, the slit is perpendicular to the long side of the grating, which isn't long once you view it from 75°. Picture 2 looks bad because the slit is parallel to the dispersion direction; this is wrong. But the problem is then according to the comment above, this wrong Picture 2 orientation was used to produce Picture 3.

@M.Farooq are you illuminating the grating from the correct side like this: i.stack.imgur.com/gsrwR.png DoesAlso can you keep your gratings crossed the same way, but rotate the pair until the slit is parallel to the short side (not the long side) of the echelle and try once more? (it should look like slide #42 in this; your $\theta_B$ is 75°)

@RobJeffries I honestly couldn't tell; the edit helps, but why not put that at the top? I also wanted to offer something actionable.

@uhoh, of course, I am illuminating the "correct" side. Echelle gratings are pretty thick-nobody can use the wrong side. Now the question is starting from picture 1, what we should we "practically" do to get a true 2D spectrum.

@RobJeffries, Yes, the textbook figures look easy but there is something tricky or practical which is missing. Please see my question with "wire transmission gratings" which will further clarify that there must be some trick which is not visible in these textbook figures. physics.stackexchange.com/questions/572299/…

@M.Farooq No, I mean from the side; In order to be illuminated correctly, it should be tiled at 75° so the light is almost pointed towards one edge of the grating. Echelle gratings are designed for a very specific direction of illumination.

@uhoh, I think I have tried this tilting as well. Look at this picture, astro.physics.uiowa.edu/iro/equipment-2/…

@uhoh, My understanding with blaze was that it will throw light in one particular direction. We are getting the correct picture, no. 1. I will try illuminating at the lower side of the grating.

@M.Farooq your understanding should be that if you don't get the direction correct, you are likely to just get crap results.

@uhoh, You point is valid. Will check if I can see a decent result.

Okay good luck, I have some background in echelle gratings and they can't be treated like lower order gratings. Please look for an arrow somewhere on the grating itself. You have to use the large tilt but you also have to do it from the correct side. There should be an arrow somewhere.

Imagine you give a detailed procedure for an organic synthesis to someone, and they say it doesn't work. After a long discussion you find out that they skipped several steps because "according to their understanding" those steps weren't necessary.