#1 Period of MEG - Case CLOSED
First light has LEG first orders exactly where they should be within a micron:
```LEG 1st order distance = 5366.55*(12.398/1.486)/9921 = 4.513 mm
From first-light HSI image measured: 4.513 mm  (!)```

The MEG first order HSI image is at a distance of 11.300 mm equivalent to ~3962 A. Subassembly prediction is 4000.72 A with ~4 A error. The subassembly is based on measured angles in LR diffraction setup and HeNe laser being 6328 A wavelength. Estimated error is 0.1 percent or 4 A. Another reason to believe the subassembly is that Mark Schattenburg set up the MEG period using measurements of angles in his lab (holography) and a 351 nm laser. That the LR gave 4000.x and Mark was shooting for 4000 suggests at most a few A error. Besides subassembly error other possibilites are:
• MEG image at gap or other HSI problem area [Kathy's HSI thoughts]
• Zero-order on MEG first light image is at the edge - maybe zero-order location is not accurate?
• MEG periods changed due to exposure to heat source shrinking polyimide more in the middle than edges
• Period changes in vacuum due to low humidity?
• It's a Mystery!

8/24/96: Herman makes progress on it: "Brad Wargelin reports in his 2nd floor shift report that the dispersion distance [for 5th order MEG - dd] was found to be 55.933 mm from 0th order [I assume this is along-dispersion-axis distance and not Y-axis-only distance - dd] and that the image was at an angle of 3.96 degrees from the horizontal. If this angle is added to the estimate of the stage to dispersion angle, one gets an angle of 4.81 degrees as the angle between the LETG and MEG dispersion directions, which is within the tolerances (5.0 deg +/- 0.5 deg). The period of the MEG is then estimated to be 4000.92 A [? see calculations below - dd], which is within the tolerances of the expected period, which is 4000.72 ."

``` Grating equation for normal incidence:
lambda
sin ( theta_diffraction )  =  m  x  --------
p
for flat focal surface:
dispersion distance
theta_diffraction =  atan ( --------------------- )
Rowland diameter

Rowland diameter for TMA/TOGA is 5366.55 mm based on measurements
and TMA focal length.

LEG Period  (first-light data)
-----------------------------
sin ( atan(4.513/5366.55) ) = 1 x (12.398/1.486)/p
p = 9921.17 A   (LEG sub-assembly period = 9921.36)

MEG Period  (fifth-order MEG data)
-----------------------------
sin ( atan(55.933/5366.55) ) = 5 x (12.398/1.486)/p
p = 4002.70 A   (MEG-TOGA sub-assembly period = 4000.72 +/- 4A)
```

Note that we're getting into the regeme where knowing the 12.398 AkeV factor and the X-ray line energy (1.486 keV) to the 0.1% level is required!

8/28/96: Dan writes: Based on beam-centering measurements of the LEG, MEG, and HEG +-1 and 0 orders the following parameters should accurately predict the location of TOGA grating images:

``` Grating     Roll angle     Period

LEG        -0.9073 deg    9915.7 A

MEG         3.9489 deg    4004.5 A

HEG        -5.9974 deg    2002.3 A
```

The periods are based on Al-K measurements and constants used are: 12.398 AkeV, 1.486 keV, 5366.55 mm. These values will be used to update the awk script (rehearsal.pl ?) that produces detector locations for measurements at rehearsal. The angles of roll are positive moving from facility Y axis towards the facility Z axis.