David Norris

QOI Rotation, Fall 2005

Orozco Lab

 

A Measurement of the Pointing Stability of a Laser

 

A planned Francium experiment will utilize an ultra-stable atomic trap.  The trap requires a laser with spatial precision on the atomic scale.

 

In this project we made a preliminary measurement of the stability of a tabletop laser using a position sensing photodetector and investigated the limits of the detector’s sensitivity.

 

 

Equipment

 

  • Ultra-stable commercial diode laser (helium-neon)
  • Stable optics mounting (avoid mirror mount New Focus 9811!)
  • Split detector (Thorlabs PSDM 3)
  • Oscilloscope and spectrum analyzer

 

 

Optics Setup

 

The laser beam is aimed via a series of mirrors into the split detector.  The detector contains two adjacent photodiodes, each of which outputs a current proportional to the light intensity striking it.  The sum and difference of the two currents are viewed on an oscilloscope and a spectrum analyzer.  A variable attenuator in the beam path adjusts power into the detector, while a polarizing splitter provides a second beam with which we can relate changes in detector current and lateral beam displacement.

 

 

 

 

 

 

 

 

 

 

 

 

 

 


In order to translate a change in output voltage to a real change in beam position on the detector, we measured the larger motion of the split beam’s spot on the wall.  Relating displacements by Δx/Δs = Δx’/Δs’, we found that a change of 1 V in the detector output current corresponds to a spatial displacement of approximately 1 mm at the detector.

 

 

 

 

 

 

 

 

 

 


Electronics Setup

 

The current generated in each photodiode is converted via trans-impedance amplifier into a voltage.  The voltages are combined in sum and difference operations to provide the output signals.  Assuming that the silicon photodiodes produce ~ 0.5 A of current per watt of incident light, the total current from the split detector is ~ 18 μA.  The effective gain seen in the Vdiff output, the conversion factor between current and voltage, is then G ~ 104 V/A.

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Data

 

The spectrum analyzer records the power spectral density (PSD) of the Vdiff signal, which is the power normalized to a 1 Hz bandwidth.  This is a useful way of measuring noise, as the amplitude of the noise spectrum increases with bandwidth.  Noise in the PSD is independent of frequency span. 

 

Power is proportional to V2, and the power spectrum is normalized to (divided by) 1 Hz.  Taking the square root of these gives the units of PSD: V/√Hz.  The voltage is displayed on a logarithmic scale in units of decibel volts (dBV), defined by

 

dBV =  20 log (Vsignal/ 1 V) 

 

Thus a reading of 0 dBV corresponds to a signal of 1 V, -60 dBV to 1 mV, and –120 dBV to 1 μV.  

 

The lower line in the graphs corresponds to the spectrum analyzer display with the laser switched off—a measure of noise in our electronics system.  We see that the instrument noise floor is –113 dBV, or 2.2 μV.  The analyzer cannot resolve signals smaller than this amount.

 

 

     

 

Analysis

 

The detector current falls off for frequencies above 25 Hz, indicating that vibrations in that range are too small to be displayed by the spectrum analyzer.  However, there are considerable vibrations in the < 10 Hz range, with a typical value of about –80 dBV = 10-4 V.  This corresponds to spatial displacements ~ 10-7 m.

 

In addition to the noise floor limit of the spectrum analyzer, the photodiode signals are inherently limited by shot noise, random fluctuations in the current arising from the discrete nature of the electron charge carriers.  The shot noise current is related to the output current by

 

inoise = 2√(ieΔB),

 

where i is the total current out of the detector, e is the charge of an electron, and ΔB is the bandwidth of the measurement.  In our graph, this corresponds to a limit at 8.5 x 10-8 V/√Hz., or –141 dBV/√Hz.  However, this is well below the noise floor of –113 dBV/√Hz of our spectrum analyzer, so the shot noise limit did not affect this measurement.

 

 

Conclusions

 

Much work remains to be done to ensure that the laser is stable enough for use in a high-precision trap.  Its mounting must be improved, and it must be better isolated from environmental noise.  Also, more sensitive equipment is needed to determine stability on the atomic scale.  The current noise floor of 2.2 μV limits the detection of vibrations in the detector to ~ 10-9 m.  If this noise floor is lowered, the detector shot noise ( ~ 10-11 m oscillations) may begin to limit the measurement.