Currently, the best method to measure collimation in the tunnel is to use the large aperture shear plate (Thorlabs SI500).

Shear Plate Measurement Procedure

The shear plate must be used with the fiber laser in the tunnel. The pulsed laser is far to short to get interference. Even when uncompressed, the pulsed laser does not have a long enough coherence length to produce interference.

The shear plate nicely fits on top of the rail camera stage. It needs to be placed as high as possible; bolt some base places/spacers to the bottom so that it just barely fits beneath the enclosure. The diffuser screen needs to be removed to get the assembly into the rail camera enclosure

  1. Make sure the fiber laser is aligned to the rail camera.
  2. Move the rail camera to the downstream position.
  3. Remove the diffuser screen from the shear plate.
  4. Place the shear plate on the rail camera stage somewhere downstream of the PBNear/Far enclosure. The reflected beams should head towards the wall.
  5. Reinstall the diffuser screen.
  6. Setup a camera with a cctv objective imaging the diffuser screen. Use the rail cameras ethernet port on the stage for this camera.
    1. Disconnect the rail camera and connect the new camera there, the second port on the stage is not currently connected.
  7. Send the fiber laser and look for the interference pattern.
    1. The pattern is dim, adding black foil around the setup may help reduce the backgrounds.
    2. Taking a background and subtracting it helps a lot, the horizontal line will still be visible.
    3. See Figure 1 for an example of what the pattern should look like.
  8. Adjust the longitudinal position of the first lens in the expanding telescope in the laser room until the interference pattern is parallel with the line on the diffuser screen.
    1. Moving the lens further apart will make the laser converge.
    2. Moving the lenses closer together will make the laser diverge.
    3. See Figure 3 for an example of a well collimated interferogram. 

Divergence Calculation

The angle of the interference pattern  \(\phi\) is related to the radius of curvature of the wavefront  \(R\) at the diffuser screen by

\[R=-\frac{sd}{\lambda\tan\phi}\]

with the fringe spacing given by

\[d=\frac{\lambda}{2\delta(n^2-\sin^2\alpha)^{1/2}},\]

where  \(\lambda\) is the wavelength,  \(n\) is the refractive index of the shear plate, \(\delta\) is the wedge angle, and \(\alpha\) is the incident angle on the plate. The lateral shear distance is given by

\[s=t\frac{\sin 2\alpha}{(n^2-\sin^2\alpha)^{1/2}},\]

where  \(t\) is the shear plate thickness.

Combining everything, the radius of curvature is

\[R=-\frac{t\sin 2\alpha}{2\delta\tan\phi(n^2-\sin^2\alpha)}.\]

Positive radius of curvature means the beam is diverging. The angle of the interference pattern is measured from the positive x-axis to the fringes.

The Thorlabs SI500 shear plate has \(t=13\,\mathrm{mm}\) ,  \(\delta=-48.5\,\mathrm{\mu rad}\) , and is made of fused silica with  \(n=1.4536\) at the 785nm wavelength of the fiber laser. The angle of incidence is nominally 45deg. The radius of curvature is then given by 

\[R\mathrm{[m]}=\frac{83.1}{\tan\phi}\]


For details, see https://doi.org/10.1364/AO.16.002753, but note the difference in sign of  \(\delta\) , the fringes are tilted the opposite direction for converging/diverging.

Figure 1: Typical interferogram in the tunnel, the laser is not collimated here. The beam is diverging.


Figure 2: More obvious interferogram, the laser has even worse collimation. The beam is diverging.


Figure 3: Interferogram when the laser is well collimated.

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