Spectra related

Spectrometer

Fiber Optic

  • The fiber optic bunlde has ~30 fibres, arranged linearly at one end circularly at the other

Grating

Groove density Spectral range Resolution
1200 grooves/mm 350 - 900 nm 14nm/mm @$\rm{H}_{\beta}$

Camera

Motor

  • For control of the grating angle the spectrometer uses Thorlabs Z612:

Spectrometer


Grating2.png

Some useful equations for the spectrometer are shown below:

  • Grating equation:
\begin{equation} 10^{-6} k n \lambda = \sin{\alpha} + \cos{\beta} \end{equation}
  • Equation for deviation angle:
 \begin{equation} \rm{D}_v = \beta - \alpha = \rm{D}_{v,x=0} + \tan^{-1}{\left(\frac{x}{\rm{f}_2}\right)}\end{equation}
where $\rm{D}_v$ is the deviation angle, $\alpha$ and $\beta$ are the angles between the normal to the grating and the incoming and outgoing light beams.
  • Dispersion:
 \begin{equation} \frac{d\lambda}{dx} = \frac{10^6 \cos{(\beta)} \rm{f}_2}{k n (\rm{f}_2^2 + x^2)} \end{equation}
where $\lambda$ is the wavelength, $x$ is the position on the CCD, $\beta$ is the angle between the outgoing light beam and normal to grating, $k$ is the order of diffraction $n$ is the groove density and $f_2$ is the focal length from the lens to the camera.

From calibration parameters were found to be:

Camera focus Camera angle fibre diameter on CCD
19.9mm 4.6mm 4.34 pixels or 0.42nm

Spectrograph

The spectroscope is small transmission grating which can be placed in the filter wheel of the SBIG - 8XME camera

  • Grating equation:
\begin{equation} \lambda k n = \sin \theta \end{equation}
where $k$ is the order of diffraction, $n$ is the number of slits and $\theta$ is the angle of diffraction.
  • Angle of diffraction:
 \begin{equation} l \tan \theta = x \end{equation}
where $x$ is the position on the CCD and $l$ is the distance on the grating from the CCD.

From calibration parameters found to be:

Slits distance from CCD
200 26.8mm

Beam Splitter

  • The beam splitter used is a pellicle beam splitter which transmits 70% and reflects 30% of the light.
Beam_Splitter.png
  • The aim of using a beam spitter is that it can be used such that the position of the beam on the CCD camera can be aligned with the position of the beam on the optical fibre. Therefore, the beam can be positioned on the camera such that the optical fiber has a maximum intensity.
  • The CCD camera can also be focussed such that both itself and the optical fibre are in focus. This allows quick alignment and focus when attached to the telescope.

  • The set up of the optical table used for calibration of the camera and the optical fiber is shown below. This uses a low power laser to align and focus the beam splitter and optical fiber.
Optic_Table.png
  • The laser used has a maximum output of 1 mW, and operates in the range of 620-690 nm.
  • As the laser will be focussed onto a point defined by
\begin{equation} w = \frac{4 \lambda f}{\pi D}, \end{equation}
  • where w is the diameter of the focus, $\lambda$ is the wavelength, $f$ is the focal length and $D$ is the diameter of the beam before focus. The expected focus is thought to be smaller than an individual fiber, therefore, at best focus only one fiber should be illuminated.
  • Before starting the calibration the intensity of the laser beam should be reduced so that it will not damage the camera. This can be done by using the diffuser and paper in front of the beam.
  • The lens used is a 3 Dioptre lens which give 1/3 m focal length.
  • The aim is to replicate the f-number (f#) of the telescope with the lens, where f# = f/D, where f is the focal length and D is the diameter of the aperture. The telescope has a f# = 10, therefore the beam size of the laser must be 33.3 mm to achieve the same f#.

Alignment procedure

  1. Initially the beam is to be aligned such that it is as straight as possible going into the camera and optical fiber.
    1. Start by closing both of the irises.
    2. adjust the first mirror, top left in diagram, so that the beam is as central on the first iris as possible.
    3. then open the first iris so that the beam can be seen on the second iris.
    4. adjust the second mirror, bottom left in diagram, such that the image is as central as possible on the second iris.
    5. close the first iris and repeat the above steps such that the beam is aligned as straight as possible.
  2. Aligning the beam to the camera and optical fiber.
    1. Initially the approximate best focus should be found by adjusting the beam splitter box backward and forward until the image of the laser is as small as possible on the camera.
    2. Then locate the spectral line of the laser using the spectrometer.
    3. Then by adjusting the second mirror, bottom left in image, complete a horizontal scan of the beam across the camera. Whilst doing this record an image of both the camera and the spectrometer for each change in position on the camera.
    4. Plot the average intensity of the spectrum against the position on the camera to find the position at which the intensity is at a maximum, then move the beam to this horizontal position.
    5. Repeat the process of a horizontal scan, but this time scan vertically. Once vertical scan is completed set the beam position to the horizontal and vertical positions found.
  3. Focus of beam on camera and fiber.
    1. To set the focus images can be taken of the camera and spectrum for different focal lengths. However, as the focus is smaller than an individual fiber, the maximum intensity of the spectrum will remain the same as the beam is scanned across the aperture of the fiber bundle.
    2. Therefore, to find the best focus, the horizontal alignment in step 2. can be repeated for a selection of focal lengths around approximate focus point.
    3. By then selecting an individual fiber within the spectrum, the width of the scan plots for each of the focal lengths can then be used to find best focus. i.e the minimum width of a scan is at the best focus.
  4. The alginment procedure in step 2. can then be repeated to acheive maximum intensity.

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Topic revision: r14 - 05 Aug 2016 - JosephBayley

 
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