This article describes a simple laboratory spectroscopy test bench to obtain resolving powers as high as R = 150 000. The optical set up is basically composed of an échelle diffraction grating, a doublet achromatic lens, a beam splitter, an optical fibre and a CCD camera. Among others, this experiment allows to discern and study the longitudinal emission modes of diode lasers. Our 20′ video Building a spectroscopy high resolution experiment explains in details the bench implementation
- Thorlabs AC508-500-A – f = 500.0 mm, Ø2″ Unmounted Visible Achromat, ARC: 400-700 nm
- Thorlabs AC508-400A – f = 400 mm Ø2″ Unmounted Visible Achromat, ARC: 400-700 nm
- Thorlabs GE2550-0863 – Échelle Grating, 79 Grooves/mm, 63° Blaze, 25 x 50 x 9.5 mm.
- Thorlabs GE2550-0875 – Échelle Grating, 79 Grooves/mm, 75° Blaze, 25 x 50 x 9.5 mm.
- Fibres: core 25 and 10 um, 3 m length, with SMA connectors on both ends.
- Beam splitter: Thorlabs BS013 400-700 nm Broadband Non-Polarizing Beam splitter Cube 25.4 mm x 25.4 mm x 25.4 mm
- Alignment collimator. A photographic objective Aperture Ø: 50mm , 500mm focal length and 20mm eyepiece and focus calibrated at infinite.
- Camera CCD: SBIG ST1603ME, 1530 x 1020 squared 9um pixels. CCD sized: 13.8 x 9.2 mm.
- Microscope: 6.3x objective, 10x eyepiece
- Green laser: wavelength 532 nm
- Spectral lamps: Hg pen lamp and Na discharge lamp.
- Mechanical parts: rails, posts, translation linear stages, water level,…
Figure 1 shows the optical layout of the experiment. The échelle grating has been set up in Littrow configuration where the angles of the incident and diffracted rays with respect to the échelle are the same. A beam splitter has been introduced to get this arrangement. The optical fibre is illuminated by the diode laser, its output end acts as a light source and is placed at the focal plane of the lens. The light beam is reflected by the beam splitter before reaching the lens. The collimated beam after the lens goes to the échelle grating and the diffracted beam is focused on the CCD camera through the beam splitter. The blaze angle of the grating is 63 but it was turned to 62 degrees to centre the diode laser wavelength (532 nm) on the optical axis. The configuration works at the order 42. There is no need of a cross-dispersed because we observe tiny wavelength variations of lasers which stay in the same diffraction order.
The beam splitter was introduced to work in Littrow mode but at the cost of some drawbacks: first, only 50% of the incoming light goes to the collimator-échelle group. The échelle efficiency is about 50%, to that we have to consider that the échelle didn’t cover all the collimator aperture. We estimated a vignetting of 60 %. So 25% x 0.4 = 10% is directed to the detector. But another 50% is taken by the beam splitter again, so the resulting beam reaching the detector is only 5%. To that we have to subtract another 4% losses by the doublet and around 8% more by the reflection losses in the beam splitter. At the end, around 4.5% of the original beam reaches the CCD. Another problem is the introduction of aberrations by the beam splitter. These aberrations may significantly reduce the resolving power of the spectrograph.
Figure 2 shows the spot diagram for 4 wavelengths: 532, 530, 528 and 526 nm. The first is the laser wavelength; the fourth is the extreme wavelength of the free spectral range of order 42. Note the rapid degradation of the image quality at the extreme wavelengths. However, in our case we have worked close to the centre of the field where the aberrations are close to the diffraction limit (Figure 2, right).
Figure 3. Spot diagrams. Left: all wavelengths. Right: central wavelengths
In order to accurately measure the resolution, the pixel matching (projection of the monochromatic image of the fibre, or point spread function) should cover between 2.5 and 3 pixels of the CCD. Since one of the fibres is very small (10 um core diameter) we tried to use a detector with the smallest pixel size. The SBIG 1603ME has pixels of 9 um. With this pixel size the image of the 25 um fibre covers 2.8 pixels. However, for the 10 um fibre, the pixel matching is only 1.1, well below the required 2.5. The measurements with this under-sampling are therefore quite inaccurate. For this case we have placed a divergent lens between the beam splitter and the detector to increase the size of the image of the fibre on the CCD. The drawback was a small degradation of the image quality and therefore a degradation of the resolution.
The complete implementation of this experiment is better shown in this 20′ video under the title “High resolution spectroscopy experiment”.
It is important to mention that the the green laser used here plays important different roles:
- it is used to align the optic;
- it is used to identify the brightest order of the echelle to set it in its Littrow configuration; and finally
- it is the primary source of light for this very high resolution experiment.
Theoretical resolving power
The spectral resolution in Littrow configuration takes a simple form:
where f is the focal distance of the doublet lens, w the slit width and θ the incident (= diffracted) angle to the grating.
Table below shows 4 examples using 2 doublets, 2 fibres and 2 gratings. Note that the resolving power does NOT depends of the number of grooves but by the Littrow angle!
|f = 500 mm, w = 25 µm, θ = 62o||75 000||85 000|
|f = 500 mm, w = 10 µm, θ = 62o||188 000||116 000, 140 000 with divergent lens|
|f = 400 mm, w = 25 µm, θ = 62o||60 000||68 000|
|f = 400 mm, w = 25 µm, θ = 75.2o||121 000||106 000|
Measured resolving power
We have used the standard method to measure the resolving power of the arrangement: we measure the spectral coverage of the point spread function (image of the fibre) on the detector. The resolution is given by the ratio of this spread to the wavelength of the light beam, in other words R = /. Now to measure the spectral coverage of the image of the fibre we have to find and observe with the spectrograph an adequate doublet or triplet from a known spectral lamp. We have used the doublet emission lines of the Hg lamp (576.96 and 579.07 nm). Once we have recorded these lines on the CCD, we can deduce the spectral dispersion per pixel of the experimental set up. With this value, we measure the FWHM (full width half maximum) of any of the Hg lines and apply the equation above. The last column of the Table above shows the resolutions we measured with our experimental set up. Note that the resolving power for the configurations using the 25 um fibre and the 62 deg échelle is slightly higher than the theoretical one. This effect is due to the circular shape of the fibre: the resolving power equations are derived by assuming a rectangular slit uniform illuminated. A circular fibre may be composed by a number of slides [parallel to the dispersion direction on the CCD. Each slide has its own “width”. Only the central slide has the width of the equivalent slit. The other slides decrease their width. Therefore there is an associated resolving power for each slide. The resolution of the slides on the poles has a higher resolution than the one in the equator. In a rectangular slit all the slices contribute with the same resolution. Therefore the the average resolution for all slices in a circular fibre is higher than the slit counterpart. This increase in resolution is around 20 % with respect to the slit counterpart. The price to pay for this increase is a reduction in flux efficiency: the fibre shape picks up less than photons than the slit shape. The amount of vignetting by the circular shape is precisely 20%!
When using a 10 um fibre, the sampling factor by the detector is well below the required one (2.5 to 3 pixels per FWHM of the PSF). The image of the spectral line can felt in one pixel or covering 2 pixels. This under-sampling creates a big error in the measurement of the FWHM of the spectral line (PSF).
In the configuration using a 25 um fibre but with another échelle where the blaze angle is bigger (75.2 deg), we obtained resolving powers below the theoretical one. Since we did just one test, we suspect that the measurement of the dispersion per pixel was not properly done.
Wavelength vs. intensity with a green laser (532nm).
Most of green diode laser pointers are not monochromatic but they emit radiation in several longitudinal modes having slightly different wavelengths. These modes are also polarized. The number of modes, the intensity and the separation between them depends largely in the type of laser cavity. The mode separation is about 0.05 nm only.
To separate these modes you need a spectrograph with a minimum resolving power of R=10 000. However, the lateral lines separation is so small that a powerful microscope is needed if you want to observe them with your eye instead of the CCD. With our spectrograph working at resolutions beyond 60 000 their visual observation is simpler and more spectacular.
The image below shows a sequence of 7 exposures starting (top) with a current of 100 mA feeding the green laser and with increases of 10 mA up to 160 mA (bottom). In this current range there are 4 modes in total but they do not lase simultaneously, they appear as a function of the current applied to the diode. The first mode (left) only appears with current 100 mA or less, while the forth mode (right) appears first with 110 mA very weak but increases in intensity when increasing the current.
Layout used for this observation: Fibre 10um, collimator: 500 mm focal length, échelle 79gr/mm working at 62 degrees to centre the 532 nm and a CCD camera SBIG 1603ME with 9 um square pixel. Under this configuration we got a dispersion of 2.547×10-3 nm/pixel. Theoretical R: 188000, Measured R: 120000
Figure 4 shows the wavelength shifts for each mode as a function of the diode current intensity. we measured roughly a factor of 2.5×10-4nm/mA
Observing the well know Na doublet D1 & D2
In astronomical observations, the sodium doublet appears in lots of spectra. When quickly analysing the spectrum on the CCD or its respective graphical profile, the separation of the D1 and D2 lines (588.9950 and 589.5924 nm) tell us a rough idea of the resolving power of the spectrograph. Usually with resolutions of few hundreds the doublet is barely resolved. At 20 000 you can widely resolve the doublet and detect the Nickel line in the middle. Figure 5 shows the Na doublet as seeing by our test bench
We have built a test bench spectrograph with an échelle grating but without cross-disperser to study the behaviour of the longitudinal modes of pointer green diode lasers. With a proper pixel sampling of the PSF (25 um fibre), we measured resolving powers a bit higher than the theory. The discrepancy is due to the fact that the fibre has a circular shape instead of a rectangular slit.
In one setup using a f 500 mm doublet achromat, a 10 um fibre and an R2 (63 deg blaze) échelle we could reach 140 000 of resolving power. The theoretical value is 188 000. The big discrepancy was caused by the strong undersamplig of the 10 um fibre, only 1.1 pixels per resolution element (FWHM of the PSF).
Using a low power microscope (60x), we can observe with the naked eye the longitudinal modes of a 532 nm diode laser and study their behaviour as appearance, polarization and intensity as a function of the current feeding the diode.
Gerardo Avila and Carlos Guirao
European Southern Observatory
Experimenting with Very High Resolution by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.