I How to couple light from a very small source into spectrometer?

[magic]

TL;DR Summary

Light source is <1 mm in size. The objective is to couple light into spectrometer with a magnification of 10x and record a spatially resolved 2D spectrum with a CCD camera.

Hello all,

I am facing challenges in coupling light from a very small source, 1 mm in size, into a spectrometer. The spectrometer is about 660 mm long, Czerny-Turner geometry, with grating size about 55 mm. The challenge is to record a spatially resolved spectrum with a 2D (about 1000x1000 pixel) camera.

I have a 10 mm focal length aspherical lens (flat side facing the light source) and another plano-convex lens with 200 mm focal length (flat side facing the spectrometer slit).

How can I design the optics so that I get:

1. Maximum light from my source into the spectrometer.
2. What distances do I need between the first lens and second lens, and the second lens and the slit? Where should the camera be placed at the exit port?
3. What does it mean that the F# of my entrance optics must match the F# of the spectrometer? MY 10 mm lens is also 10 mm in diameter, and the 200 mm lens is 50.8 mm.

I currently have the entrance optics set up such that the image plane of the light source is at the slit. However, when I focus my camera at the exit port, I get great spectral resolution, 20-30 pm, but I don't think I am getting the actual image of the light source, but rather, something smeared/averaged.

I can not find any good resources for this online, and have tried hand calculations to get an 8x magnification (source->first lens=15mm (intermediate image 30 mm after first lens), first lens->second lens 330 mm, second lens->slit 600 mm).

What am I doing wrong and how can I approach this problem?

 

[Drakkith]

3. What does it mean that the F# of my entrance optics must match the F# of the spectrometer? MY 10 mm lens is also 10 mm in diameter, and the 200 mm lens is 50.8 mm.

I haven't really worked with spectrometers before, so take what I say with a healthy grain of salt. I believe the incoming light is collimated prior to passing through a dispersive element like a grating. In order for this to happen, the optics used to focus the light down into the slit needs to match the optics inside the spectrometer used to collimate the light. This requires matching the focal length of the external optics* to the internal optics, otherwise the light isn't properly collimated. In addition, it looks like the f-number is also important in maximizing the amount of light reaching the grating for both throughput and resolution. A mismatch may result in some light not being reflected by the collimator (the cone of light is too wide) or the grating not being illuminated fully (the cone of light is too narrow).

See here: https://physics.stackexchange.com/questions/799542/about-the-focal-length-and-f-of-spectrometers

2. What distances do I need between the first lens and second lens, and the second lens and the slit? Where should the camera be placed at the exit port?

What is the focal length of the optics inside the spectrometer? You may have two different focal lengths, one for the collimating mirror and one for the focusing mirror.

*Note that object-lens-spectroscope distances matter here. A lens with a focal length of 10mm will NOT produce a image 10mm behind itself unless the object is placed at infinity. So the 'true' focal length of the imaging optics will depend on the distances between everything.

 

[BvU]

1. Maximum light from my source into the spectrometer.

TL;DR Summary: Light source is <1 mm in size. The objective is to couple light into spectrometer with a magnification of 10x and record a spatially resolved 2D spectrum with a CCD camera.

light from a very small source, 1 mm in size

Is there any information available about the angular distribution of the intensity ? (see here and here) ?

3. What does it mean that the F# of my entrance optics must match the F# of the spectrometer?

Basically, in a Czerny-Turner like (classical picture from here but most likely stolen from here):

the optics create an image of the entrance slit (B) on the exit slit (F). The image is dispersed: images for different wavelengths end up at different positions and a spectrum is obtained by (very slowly) rotating grating D and measuring the light intensity after the exit slit versus the angle.

Entrance slit B is at the focus of mirror C that creates a parallel beam at grating D. So your instrument has an F/D of about 1/11 (55/600). If the incoming beam (AB) has a larger angle, intensity is lost. If the angle is smaller, less of the grating is used resulting in lower resolution of the spectrometer.


In a CCD Spectrometer, the exit slit is replaced by a CCD (see one here). So I am surprised by your

when I focus my camera at the exit port, I get great spectral resolution, 20-30 pm

But I suppose you have removed the exit slit and can't remove the camera lens. (right ?)

calculations to get an 8x magnification (source->first lens=15mm (intermediate image 30 mm after first lens), first lens->second lens 330 mm, second lens->slit 600 mm).

I'm still chewing (rusty) on your point 2. Note that magnification of the image isn't the key: you want to match the angle. Which (thread here about etendue -- @hutchphd , @Andy Resnick and @Drakkith) isn't all that easy.



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[hutchphd]

TL;DR Summary: Light source is <1 mm in size. The objective is to couple light into spectrometer with a magnification of 10x and record a spatially resolved 2D spectrum with a CCD camera.

I can not find any good resources for this online

This is a very "slippery" subject because there are too many adjustments during design and they interact in ways that are sometimes counterintuitive and never in your favor.. I recommend the various technical notes from Edmund Optical as a place to start.. The notion of etendue is exactly at issue here and fundamentally the limits are thermodynamic (or information- theoretic, if you prefer). Along the system, anything you do will increase the etendue so the best you can do is often the least. So take a look at the Edmund stuff and previous work here at PF to generate some specific questions.

 

[magic]

1. Maximum light from my source into the spectrometer.

Is there any information available about the angular distribution of the intensity ? (see here and here) ?

3. What does it mean that the F# of my entrance optics must match the F# of the spectrometer?

the optics create an image of the entrance slit (B) on the exit slit (F). The image is dispersed: images for different wavelengths end up at different positions and a spectrum is obtained by (very slowly) rotating grating D and measuring the light intensity after the exit slit versus the angle.

Entrance slit B is at the focus of mirror C that creates a parallel beam at grating D. So your instrument has an F/D of about 1/11 (55/600). If the incoming beam (AB) has a larger angle, intensity is lost. If the angle is smaller, less of the grating is used resulting in lower resolution of the spectrometer.

In a CCD Spectrometer, the exit slit is replaced by a CCD (see one here). So I am surprised by your

But I suppose you have removed the exit slit and can't remove the camera lens. (right ?)

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My light source currently is a mercury calibration lamp (https://www.newport.com/p/6035?srsltid=AfmBOopIUA0iZcadEMOt7YoFZIz0luJPB-ErLXOGu57PrzqtFYV1kGbH). Inside the lamp are two rods along its length that emit the light. Here is what the image of the light source looks like:



I am trying to image that onto my CCD after it passes through the spectrometer. I *should* see on my recorded image, for each emission line, a break in the center vertically that corresponds to each rod therefore allowing me to have both spectral (horizontally along the CCD) and spatial (vertically along the CCD) resolution. However, I only see a single line which tells me that the image is smeared.

I think my F# is matching with my current setup, since I can see that I have about 80% of the grating illuminated. And yes, the exit port has no exit slit because I would like to record the entire bandwidth at once ~ 6 nm. My camera (with a bare CCD) is completely detached from the spectrometer and rests on translation and tilt stages. So there are three separate components that I am trying to combine: entrance optics, monochromator, and ccd camera.

he optics create an image of the entrance slit (B) on the exit slit (F)

This is what I also understand about spectrometers, which was why I've been trying to adjust my entrance optics so that the image of my light source is at the entrance slit while also satisfying the F# criteria.

So now I am wondering, does it make more sense to image my light source onto the grating instead?

 

[BvU]

Somehow more questions than answers, I'm afraid sorry about that !

I'm a bit disoriented: how can a lamp like this

cause an image like this

? Setup ? dimensions ?

And what makes you say your light source is < 1 mm ?

In the lamp info I find a mount that suggests the lamp is to be positioned right at the entrance slit (which I assume is verical) in a vertical orientation:

I am trying to image that onto my CCD

As opposed to creating an image of the entrance slit ? Why ?

I *should* see on my recorded image, for each emission line, a break in the center vertically that corresponds to each rod therefore allowing me to have both spectral (horizontally along the CCD) and spatial (vertically along the CCD) resolution. However, I only see a single line which tells me that the image is smeared.

Aren't mirrors C and E cylindrical in your monochromator ? What would cause focusing in the vertical direction ?

I only see a single line which tells me that the image is smeared.

single line in the horizontal direction or in the vertical direction ?

entire bandwidth at once ~ 6 nm

Would that be around the Hg lines at 433.92, 434.75 and 435.835 nm ?

when I focus my camera at the exit port, I get great spectral resolution, 20-30 pm

suggests you get very sharp vertical lines. Right ?
(and what do you get in #5 with the bare ccd ?)

My camera (with a bare CCD) is completely detached from the spectrometer

So how do you ensure the ccd is in the focal plane of mirror E ?


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[magic]

I'm a bit disoriented: how can a lamp like this
View attachment 357983
cause an image like this View attachment 357984 ? Setup ? dimensions ?

And what makes you say your light source is < 1 mm ?

1. The lamp is used head-on. Here is the ROI that should be about 1 mm out of the entire 6.4 mm diameter:

In the lamp info I find a mount that suggests the lamp is to be positioned right at the entrance slit (which I assume is verical) in a vertical orientation:

2. Yes, I am not using the lamp as is advised, since I am trying to image the two rods inside the lamp (the rods most likely correspond to the anode and cathode?)

Would that be around the Hg lines at 433.92, 434.75 and 435.835 nm ?

3. I am working on the four emission lines near 365 nm.

As opposed to creating an image of the entrance slit ? Why ?

4. I am trying to image both! The slit to get narrow emission lines and the light source to get the spatial variations (vertically) of the emission spectrum. Something like this: https://www.sciencedirect.com/science/article/abs/pii/S0584854716302531

Aren't mirrors C and E cylindrical in your monochromator ? What would cause focusing in the vertical direction ?

5. I don't believe so. In the documentation (the predecessor of the HR640 monochromator and built many decades ago) the monochromator uses spherical mirrors, so I should get both sagittal and tangential focus.

single line in the horizontal direction or in the vertical direction ?

6. Yes, single line in the vertical direction.

suggests you get very sharp vertical lines. Right ?
(and what do you get in #5 with the bare ccd ?)

7. Yes. Here is my recorded spectrum. As you can see, I have lost all spatial variations along the vertical direction. This is with imaging my light source onto the slit.

So how do you ensure the ccd is in the focal plane of mirror E ?

8. I manually move the camera using the micrometre translation and tilt stages until I get a sharp image. So the CCD usually ends up a few cm from the exit port; the distance from the entrance slit to the first mirror is very close to the distance between the second mirror and the CCD.

 

[magic]

OK guys, I think I am slowly getting to the bottom of this. These are the spectra that I have collected from the main Hg lines (from left to right 578 & 579 nm -> 365 nm):


You can clearly see that I lose spatial resolution as I go to lower wavelengths while more-or-less maintaining spectral resolution. This leads me to believe that the grating is mounted incorrectly! There must be some incorrect tilt or something. I highly doubt that this is something physical in the lamps emission spectrum, whereby lower wavelengths are more homogeneously emitted than the longer wavelengths...

The monochromator is very old and has not been in use for many years. So much could have happened during storage or transport or whatever until it landed on my lap. I was beginning to doubt my sanity here, but I think it's back to the drawing board and really try to figure out how to bring this monochromator back to life.

I cannot thank you guys enough for your time and help. It forced me to think more closely at what I am really trying to accomplish and how to go about doing so.

Edit: It does not appear to have anything to do with the grating tilt. I think this has to do with the second mirror and the mismatch between the sagittal and tangential focal lengths. The difference between their focal distances grows with decreasing wavelengths. I don't think there is a straightforward way to solve this. I will continue experimenting, otherwise I will have to settle for 500+nm :(

 

[BvU]

Thank you for bearing up with my curiosity , triggered by memories of a long time ago...

4. I am trying to image both! The slit to get narrow emission lines and the light source to get the spatial variations (vertically) of the emission spectrum. Something like this: https://www.sciencedirect.com/science/article/abs/pii/S0584854716302531

First reaction is: you can have both only if lamp and entrance slit are at the same place. Or indeed an image and the entrance slit. In the reference they have a 1:1 image (F/3) in fig. 1, and a 2.3 : 1 (F/6) in a second system -- no mention of focal distance.

Aren't mirrors C and E cylindrical in your monochromator ? What would cause focusing in the vertical direction ?

5. I don't believe so. In the documentation (the predecessor of the HR640 monochromator and built many decades ago) the monochromator uses spherical mirrors, so I should get both sagittal and tangential focus.

Yes, I was completely mistaken . The imaging of the entrance slit on the exit slit is both vertically and horizontally in order to get maximum light out.

Your spectrum looks excellent and matches the Oriel info

It seems to me you are doing everything right, so all I can do for the spatial part is refer to experimentation: perhaps mount the lamp vertically and use narrow horizontal strips of black tape to get a clear and simpler spatial source; see if you can find its image at the exit port ...

Keep us posted !

- - - - - - -

Re:

I can not find any good resources for this online, and have tried hand calculations to get an 8x magnification (source->first lens=15mm (intermediate image 30 mm after first lens), first lens->second lens 330 mm, second lens->slit 600 mm).

Wouldn't that get you a 4 times magnification ?

And: do you need a real image? Wouldn't a virtual image at the same position allow you to collect more light from the source ?


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[magic]

Problem solved by moving back the light source's image plane away from the entrance slit until the final image after the monochromator coincided with horizontal focus. I don't suffer much light throughput by doing so (in fact, it may have even improved!). Here is the image and spectrum:



I am very pleased!

Wouldn't that get you a 4 times magnification ?

Ah yes, that's correct. My final aim is to get 8x magnification.

And: do you need a real image? Wouldn't a virtual image at the same position allow you to collect more light from the source ?

This is a great idea. For alignment purposes, I was working with the real image. I'll give this a shot. It may also allow me to reduce the telescopic length of the setup.

 

[Gleb1964]

Problem solved by moving back the light source's image plane away from the entrance slit until the final image after the monochromator coincided with horizontal focus.

I understand your problem and recognize your calibration light source, as I have worked with similar ones.
The Czerny-Turner monochromator uses spherical mirrors (not cylindrical as assumed) to transmit the image of the entrance slit to the exit slit through a dispersive element (diffraction grating). The slit image exhibits astigmatism and coma aberrations.
Coma is compensated at one wavelength in the middle of the working range by balancing the coma of the collimator mirror with the coma of the opposite sign of the focusing mirror through the angular magnification of the diffraction grating.

Astigmatism is not corrected because it does not affect the projection of the elongated input slit to the output slit. Astigmatism means there are two different focuses in the meridional and sagittal planes. The monochromator achieves a sharp focus across the slit to create sharp edges. The second focus along the slit is located a few millimeters outside the slit. However, focusing your image outside before the entrance slit significantly truncates the angular acceptance aperture of the monochromator.
Another issue is that you have a very diffused light source. The image you demonstrated was taken from a large distance. Reimaging with a micro objective would likely result in a very short depth of focus, causing significant blur.
To maximize the performance of light throughput, you need to use an additional element that induces astigmatism of the opposite sign before imaging at the entrance slit. This could be a tilted concave mirror, oriented perpendicularly to the mirrors inside the monochromator layout. However, it is difficult to design this without knowing the exact monochromator layout.