> Results of vibration versus water-flow measurements at BL7.2 on
> Tuesday, January 21, 2004:

Tom Scarvie

> The vibration measurements were performed using seismic accelerometers
> (model 731A) and power amplifiers (model P31) from Wilcoxon Research
> connected to a spectrum analyzer (HP-3563A). The analysis was then
> performed using Matlab. The bandwidth and noise specifications for the
> accelerometers, as provided by the manufacturer, are the following
> (see Wilcoxon Research Accelerometer manual for more details):

Bandwidth: 0.1 -- 300 Hz

> Noise Power Spectrum: 0.03 g/Hz at 2 Hz
>
> 0.01 g/Hz at 10 Hz
>
> 0.004 g/Hz at 100 Hz, where g is the gravitational acceleration
>
> 1% coupling between horizontal and vertical motion (not including
> mounting).
>
> The accelerometers were mounted on a "T" aluminum block that was
> securely clamped to the alignment monument fixtures on top of the
> pinhole array flange and to the bolt heads of the visible light port
> flange. The horizontal accelerometer in measurements 1. and 2. was
> parallel to the beam axis; measurement 3. is a comparison of the
> parallel horizontal orientation to the one perpendicular to the beam
> axis. It should be noted that these measurements are of the motion of
> the *housings* of the elements, and not the elements themselves. Since
> the elements are securely mounted to the housings, the data should
> give us a good picture of the magnitude of the motion, and a very good
> relative measurement of vibration for different flow settings.
>
> The frequency range of interest for these measurements was from the
> lowest possible frequencies of about 0.3 Hz (somewhere between 0.3 and
> 1.0 Hz the noise floor of the accelerometers begins to dominate) up
> through to about 400 Hz. In order to obtain higher resolution power
> spectrum data, three data sets were taken for each measurement\-\--one
> from 0-20 Hz, one from 0-100 Hz, and one from 0-400 Hz. For all the
> data a Hanning window was used and 20 power spectrums were averaged
> for each measurement (inside the HP-analyzer), to reduce the variance
> of the estimated spectrum. The HP analyzer uses a 2048 point FFT (1024
> points are kept in the power spectrum). Anti-alias filtering is
> already performed inside the analyzer.
>
> The spectrum data read from the HP-analyzer is then post-processed
> inside Matlab. Integration of the acceleration power spectral density
> provides displacement information and ultimately a cumulative
> rms-amplitude (Parseval's theorem). We usually integrate the spectra
> from high to low frequency. Each figure contains the power spectral
> density as the upper plot and the cumulative rms-amplitude of the
> vibration as the lower plot. Sensitivity of the accelerometers was set
> to 1000 V/g for all measurements, and the low pass filter in the
> amplifier of the accelerometers was set to 450 Hz.
>
> The raw measurement data is available and can be sent on request
> (contact Tom Scarvie) or downloaded from
> \\\\Als-filer\\physdata\\matlab\\srdata\\BL72\\vibration_vs_h2oflow.
>
> Let's just skip to the interesting part first and look at the plots
> that really matter:
>
> **1. Below is a comparison of the vibrations of the pinhole housing
> for "high" H2O flows of 1.5GPM to the pinholes and 3GPM to the optical
> mirror, "low" flow of 0.6GPM pinhole, 2.0GPM mirror, and no-flow (0GPM
> to both).**
>
> ![](media/image1.png){width="6.7027777777777775in" height="8.7875in"}
>
> ![](media/image2.png){width="6.7027777777777775in" height="8.7875in"}
>
> As one might expect, the vibrations got smaller as the flow was
> reduced. However, even in the high flow case, the RMS displacement is
> only about 1 µm at 1 Hz. The shutter is operated at 1/60^th^ sec,
> where the vibrational motion is only in the 10s of nanometers. There
> was a noticeable improvement when the flow was reduced, so even if we
> don't see a practical improvement in the image, at least we're "living
> clean", with the flows set as low as possible while still protecting
> the optical elements. The flows are currently set to the low-flow
> values.
>
> Now let's look at some other interesting data:
>
> **2. Comparison of vibrations of visible light port and pinhole
> assembly with "high" H2O flows of 3GPM for the visible port mirror,
> and 1.5GPM for the pinhole array:**

![](media/image3.png){width="6.83125in" height="8.965972222222222in"}

![](media/image4.png){width="6.790972222222222in"
height="8.89236111111111in"}

There are different vibrational modes, as one might expect, but the
magnitudes are roughly the same and small. At 1Hz, we have less than 1
µm horizontal motion, and 1-2 µms vertically. Above 10Hz, both are below
0.2 µms.

> **3. Comparison of horizontal pinhole motion parallel to the beam axis
> and perpendicular to it for the low-flow settings.**

![](media/image5.png){width="6.783333333333333in"
height="8.89236111111111in"}

Different modes of vibration again, but still the amplitudes are very
small.