Trial 28

Home Experiment Goals FAQ Theoretical Thermal Refraction Measuring Thermal Refraction Lateral Beam Deflection Vertical Beam Deflection Measuring Beam Deflection Optimum Beam Section Laser Camera Support Beam Mount Filter Camera & Laser Cells Components Experimental Controls Cell Installation Assembly Photos Calibration Photos Measuring the Images False Signal Simulation Phase 1 Experimental Procedure My First Trial Speculation for Phase 1 Trial 4 Trial 6 Trial 8 Dr. Osadchey's 6-11-07 Trial Trial 9 Trial 10 Trial 11 Trial 12 Trial 13 Trial 14 Trial 15 Trial 16 Conclusions for Phase 1 Trial 18 Trial 21 Trial 22 Trial 23 Trial 24 Dr. Osadchey's 11-5-07 Trial Trial 25 Trial 26 Trial 27 Trial 28 Trial 29 Trial 30 Dr. Osadchey's 12/9/07 Trials Trial 31 Trial 32 Trial 33 Results for Phase 1-B Sidereal Index Links More Links Speculation for Phase 2 Trial 34 Trial 35 Trial 36 Trial 37 Trial 39 Trial 40 Trial 41 Trial 42 Trial 43 Trial 44 Trial 45 Trial 46 Trial 47 Trial 48 Trial 50 Trial 51 Trial 52 Trial 53 Trial 54 Trial 55 Trial 56 Trial 57 Trial 58 Trial 59 Trial 60 (Denham Springs, LA) Trial 63 Trial 64A Trial 65A Trial 65B Custom Rich-Text Page Custom Rich-Text Page

Trial 28, 12/02/07

Trial 28, 12/2/07

Laser Start 11:16, Camera Start 12:57 (three restarts with 180 second timeout), Trial Start 13:06:15
Temperature 24.0 deg C @ 12:52

This trial was intended to examine the effect of a long warmup time for both the camera and laser.
Time interval variation between measurements was significant. Drift vs time fit is recommended.
Camera time is 8:00am at battery insert. The Camera clock was not reset.
Angles are measured using a cardinal degree scale, not Polar.

				MEAN				STD DEV		MEDIAN		MODE
Angle	Measure	Timestamp	Index	X	Xadj	Y	Yadj	X	Y	X	Y	X	Y
0	0	8:09:58	0:00:00	962.818	-1.44	986.508	-2.51	112.785	67.819	956	982	240	413
30	30	8:10:26	0:00:28	964.145	-0.18	986.903	-1.52	112.671	67.902	957	982	242	410
60	60	8:10:44	0:00:46	964.847	0.45	986.844	-0.86	112.703	67.849	960	982	244	409
90	90	8:11:06	0:01:08	964.075	-0.40	986.715	-0.13	112.988	67.881	958	982	242	410
120	120	8:11:32	0:01:34	966.152	1.59	985.241	-0.74	112.875	67.756	960	982	242	411
150	150	8:11:58	0:02:00	966.946	2.30	984.394	-0.71	112.702	67.700	962	981	242	412
180	180	8:12:24	0:02:26	966.806	2.08	984.102	-0.13	112.895	67.751	961	981	243	412
210	210	8:12:50	0:02:52	965.818	0.99	984.086	0.87	112.806	67.756	960	980	241	413
240	240	8:13:20	0:03:22	963.883	-1.01	983.583	1.13	112.975	67.820	958	980	240	410
270	270	8:13:42	0:03:44	962.164	-2.78	983.864	1.97	112.899	67.716	957	981	242	409
300	300	8:13:58	0:04:00	963.218	-1.81	983.346	2.33	112.543	67.724	956	980	241	410
330	330	8:14:24	0:04:26	963.072	-2.02	983.906	3.65	112.611	67.741	956	980	241	408
360	0	8:14:46	0:04:48	963.328	-1.85	983.756	4.47	112.731	67.704	956	980	242	408
390	30	8:15:14	0:05:16	964.301	-0.94	982.958	4.39	112.660	67.719	958	980	241	409
420	60	8:15:34	0:05:36	965.291	0.01	981.227	3.16	112.349	67.650	960	978	242	409
450	90	8:15:48	0:05:50	966.492	1.16	981.113	3.67	112.673	67.693	960	978	242	410
480	120	8:16:06	0:06:08	966.263	0.88	979.771	2.97	112.592	67.512	960	976	241	407
510	150	8:16:24	0:06:26	967.187	1.75	978.102	1.94	112.629	67.524	962	975	241	412
540	180	8:16:42	0:06:44	968.239	2.75	976.759	1.24	112.628	67.274	965	973	242	410
570	210	8:17:00	0:07:02	967.664	2.12	975.987	1.05	112.515	67.277	962	972	238	408
600	240	8:17:16	0:07:18	964.705	-0.89	975.854	1.55	112.595	67.384	958	974	239	412
630	270	8:17:34	0:07:36	964.038	-1.61	975.830	2.18	112.671	67.292	958	973	238	410
660	300	8:17:52	0:07:54	962.991	-2.71	975.288	2.29	112.422	67.114	957	972	241	408
690	330	8:18:10	0:08:12	963.373	-2.36	975.378	2.90	112.565	67.080	958	973	238	411
720	0	8:18:24	0:08:26	963.598	-2.18	974.597	2.63	112.422	67.325	958	972	239	411
750	30	8:18:38	0:08:40	964.263	-1.55	974.264	2.81	112.269	67.102	957	972	238	409
780	60	8:18:52	0:08:54	965.151	-0.72	972.219	1.41	112.322	67.417	958	968	241	408
810	90	8:19:10	0:09:12	965.183	-0.75	970.216	0.20	112.332	67.340	958	967	240	410
840	120	8:19:32	0:09:34	966.543	0.56	968.291	-0.98	112.333	67.426	961	964	239	410
870	150	8:19:52	0:09:54	967.377	1.35	966.732	-1.92	112.038	67.419	959	963	240	409
900	180	8:20:08	0:10:10	967.619	1.55	965.706	-2.42	111.922	67.491	960	964	239	408
930	210	8:20:22	0:10:24	967.971	1.87	965.647	-1.95	112.133	67.384	962	962	239	407
960	240	8:20:36	0:10:38	967.661	1.51	965.305	-1.64	111.946	67.372	962	962	237	407
990	270	8:20:54	0:10:56	966.304	0.11	965.378	-1.02	111.951	67.377	960	962	237	406
1020	300	8:21:08	0:11:10	965.908	-0.32	964.631	-1.24	111.623	67.352	960	962	238	404
1050	330	8:21:22	0:11:24	965.328	-0.93	963.908	-1.50	111.668	67.363	958	960	239	404
1080	0	8:21:34	0:11:36	965.700	-0.61	963.412	-1.34	111.663	67.367	959	960	240	404
1110	30	8:21:52	0:11:54	966.375	0.02	962.549	-1.59	111.485	67.444	959	959	240	403
1140	60	8:22:08	0:12:10	966.601	0.21	962.215	-1.38	111.653	67.330	960	959	239	402
1170	90	8:22:22	0:12:24	967.564	1.14	960.560	-2.49	111.547	67.216	961	956	238	403
1200	120	8:22:36	0:12:38	967.199	0.73	959.244	-3.21	111.417	67.410	960	955	240	405
1230	150	8:22:52	0:12:54	968.328	1.82	959.884	-1.95	111.344	67.242	962	956	239	403
1260	180	8:23:08	0:13:10	968.264	1.73	959.753	-1.60	111.495	67.160	962	958	239	404
1290	210	8:23:20	0:13:22	967.585	1.01	959.568	-1.25	111.383	67.257	961	956	239	401
1320	240	8:23:34	0:13:36	966.922	0.32	959.672	-0.67	111.451	67.165	960	958	241	402
1350	270	8:23:46	0:13:48	964.683	-1.98	960.249	0.64	111.589	67.231	958	958	238	403
1380	300	8:24:06	0:14:08	965.211	-1.48	960.336	1.25	111.422	67.180	958	956	239	402
1410	330	8:24:18	0:14:20	965.538	-1.19	959.887	1.40	111.532	67.170	958	958	240	404
1440	0	8:24:34	0:14:36	965.893	-0.87	959.639	1.71	111.513	67.165	960	956	238	401
1470	30	8:24:48	0:14:50	965.753	-1.04	958.965	1.53	111.470	67.158	960	956	239	404
1500	60	8:25:00	0:15:02	965.897	-0.93	957.426	0.53	111.417	67.315	960	955	240	404
1530	90	8:25:14	0:15:16	966.165	-0.70	956.392	0.05	111.369	67.415	959	954	237	404
1560	120	8:25:28	0:15:30	967.627	0.74	955.906	0.05	111.241	67.394	961	954	238	404
1590	150	8:25:40	0:15:42	968.024	1.10	955.485	0.17	111.218	67.327	962	954	238	405
1620	180	8:25:54	0:15:56	968.373	1.41	954.991	0.24	111.265	67.328	961	952	239	406
1650	210	8:26:08	0:16:10	968.075	1.09	955.116	0.86	111.149	67.272	960	952	239	405
1680	240	8:26:20	0:16:22	966.250	-0.77	955.215	1.44	111.375	67.355	960	951	239	401
1710	270	8:26:32	0:16:34	966.980	-0.10	954.538	1.57	111.029	67.155	960	951	238	401
1740	300	8:26:54	0:16:56	966.433	-0.68	954.616	2.41	110.960	67.238	960	951	240	401
1770	330	8:27:12	0:17:14	966.067	-1.08	954.732	3.12	110.839	67.190	959	952	239	401
1800	0	8:27:26	0:17:28	967.110	-0.16	954.890	4.76	110.762	67.167	960	951	240	401
1830	30	8:28:08	0:18:10	967.731	0.45	954.730	5.40	110.774	67.083	960	952	238	401
1860	60	8:28:22	0:18:24	967.060	-0.24	954.066	5.18	110.704	67.068	962	950	240	402
1890	90	8:28:32	0:18:34	967.949	4.35	952.971	-32.22	110.539	66.908	960	950	239	402

A second order polynomial fit is used as an approximation for drift vs. time.
0 deg = north.

	X	Y
a	-3464.4	-28509
b	286.3	-2822.4
c	964.17	989.93

average
Measure	Xadj	Yadj
0	-1.19	1.62
30	-0.54	1.84
60	-0.20	1.34
90	0.80	0.26
120	0.90	-0.38
150	1.66	-0.50
180	1.90	-0.53
210	1.42	-0.09
240	-0.17	0.36
270	-1.27	1.07
300	-1.40	1.40
330	-1.52	1.91

r	delta X	delta Y
4.205883	3.42	2.45

The Yadj value at 90 degrees is omitted from magnitude calculation and assumed unusable.

Estimated Max X		180	cardinal deg		0	polar deg
Estimated Magnitude		4.206	pixels	13.45883	microns

Estimated Max X is computed using average values.
A sinusoidal fit was determined using the least squares method.
X Y
Best Fit Sinusoid A 5.06 4.00 microns
Φ 205 283 cardinal degrees
b -0.06 -2.24 microns
σ 2.55 6.84 microns
The phase of the fitted sinusoidal function varies from the estimated by 25 degrees.
The displacement magnitude of the fitted sinusoid is 96% of the estimated magnitude.
The standard deviations of the adjusted data vs. the fitted sinusoidal function are
23% of mean adjusted horizontal and 87% of mean adjusted vertical.
The error for vertical measurements is effectively as large as the calculated result.

A least squares fit with a sinusoidal function allows a more precise estimate of phase than my previous estimates, which were made using the averaged maximum X coordinates.

The recorded image motion shows significantly lower drift than previous trials.

The adjusted coordinates were computed by subtracting out a second order polynomial fit for drift vs. time.

Note that the X coordinate value is more precise than the Y coordinate value. The X coordinates define a much tighter curve, while the Y coordinate error is equal to the estimated magnitude for this trial. This is a consistent pattern for my measurements, and is better highlighted with the low drift rate of this trial. I believe that this is due to the mount design, which creates a significantly greater change in vertical loading than change in horizontal loading for the same change in elevation.

Estimated Max X is computed using average values.

A sinusoidal fit was determined using the least squares method.
		X	Y
Best Fit Sinusoid	A	5.06	4.00	microns
	Φ	205	283	cardinal degrees
	b	-0.06	-2.24	microns
	σ	2.55	6.84	microns

The phase of the fitted sinusoidal function varies from the estimated by 25 degrees.
The displacement magnitude of the fitted sinusoid is 96% of the estimated magnitude.
The standard deviations of the adjusted data vs. the fitted sinusoidal function are
23% of mean adjusted horizontal and 87% of mean adjusted vertical.

The error for vertical measurements is effectively as large as the calculated result.