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FREQUENCY OFFSET LOCKING
Overview
In order for Absolute Length Measurement to be effective, the differential frequency (beat frequency) between prestabilized laser (PSL) and Auxiliary Laser (AUX) must remain constant.
However, over time, the AUX frequency tends to wander due to things like temperature change. Thus, we employ our frequency offset locking (FOL) system.
Frequency offset locking works by sampling light from each laser source, PSL and AUX, and combining them, in-line, to produce a beat note. The value of which corresponds to the difference between the frequencies of either laser.
This light is then fed into a photodiode, the signal from which is digitized, and sent into a digital PID control loop. The PID Controller uses this signal as the current state of the system, which is further analyzed to produce an error signal.
The error is then converted back to an analog signal, which actuates upon the frequency of the AUX laser, keeping it within the desired range.
The actuator is a temperature control, which controls the dimensions of the crystal resonator within the NPRO via thermal expansion.
Through this scheme, we hope to effectively achieve a constant frequency offset between the AUX and PSL.
Contents
Optics
Project Plan
Purpose
To implement a system that will efficiently and effectively sample and beat light from both PSL and AUX, to act as an input to the digital PID loop, which will actuate temperature servos in the AUX lasers.
Methods
Razor Blade Measurement
Razor Blade, or knife edge beam profiling, is a technique which allows manual measurement of a gaussian beam's properties (read: beam waist). A razor blade, or other reliably straight edge, is translated across a beam which is then incident upon a photodiode or power meter. As the blade is translated, corresponding measurements of blade location and power supplied to photodiode are taken. The measurements should then be repeated in the direction orthogonal to both optical axis, and original direction or translation, to give a two dimensional measurement of spot size. This measurement is repeated many times along the optical axis, preferably somewhere near the beam waist. If this is impossible, a lens may be used to create a new waist (w_f), from which the original beam waist may be calculated using ABCD matrices.
The blade position vs beam power data is then fit to V(x) = (.5*Vmax)*(1-erf((sqrt(2)*(x-x0))/wz))+c . x0 and c are offsets in x and V, correspondingly, with the independent variable being x. The other fit parameters being Vmax (maximum power available to photodiode), and wz, the spot size at the current value of z.
The spot size data is then fit to w(z) = w_o*sqrt(1 + ((z-b)lambda) / (pi*w_o2))2), where z is the independent variable (blade position along optical axis), b corresponds to an offset from zero in the x, lambda the laser wavelength, and w_o the beam waist. b and w_o are fit parameters that should be returned, lambda should be known (1064nm in our case).
This technique returns beam waist and location, relative to some point along z chosen to be zero.
Beam Profiler
Measurement using a beam profiler essentially replaces the razor blade setup, and takes measurements of spot size far more efficiently. The profilers is translated along the optical axis, where values of wz and z should be taken, again preferably near the beam waist. These data are then fit in the same way as in the razor blade measurement (see above) to yield a beam waist and location.
Measurements
Razor Blade
The razor blade measurement proved difficult, and ended up requiring six trials. Details of the final round of measurement are included here:
Setup
Data
Beam Profiler