Reproducing the Velador Experiment

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Trial 4, 5/27/07

Although it is short by one turn, this is intentional. Trial 4 is my first complete trial performed with the camera 2 setup that was successfully completed. Trials 2, and 3 were unsuccessful, and I spent three weeks discovering that digital cameras are very finicky about their power supplies. I expended the battery before the end of previous trials, introducing corrupted images and interrupting the measurement sequences. Trial 4, although it does contain errors (see the first data point), is at least complete.

Trial 4	5/27/2007
End	4:28:00 PM

ANGLE	MEAN	MEAN	STDEV	STDEV	MEDIAN	MEDIAN	MODE	MODE
	X	Y	X	Y	X	Y	X	Y
270	524.9335	601.2802	405.2579	264.1593	640	512	317	311
315	488.6915	574.2756	397.2449	274.0624	640	512	268	271
360	488.2771	576.4652	396.2062	274.3847	640	512	271	276
405	481.6264	559.5434	400.4897	274.7502	640	512	303	271
450	494.4251	571.5791	400.6143	274.5685	640	512	257	267
495	481.7756	576.2128	394.8289	277.4779	640	512	277	329
540	491.9718	567.5229	400.6394	273.2794	640	512	289	267
585	475.8098	555.9926	399.3692	277.2035	640	512	313	279
630	473.8352	558.6254	396.6194	277.9426	640	512	309	295
675	477.6395	562.7733	397.3423	278.0933	640	512	305	303
720	492.0441	568.2325	401.0668	279.1738	640	512	298	320
765	497.3925	560.6591	402.3228	276.0079	640	512	286	277
810	483.9657	553.2432	400.3102	281.1184	640	512	336	290
855	483.7713	555.2644	398.6573	281.8237	640	512	313	358
900	488.8952	552.2424	400.6411	275.5092	640	512	303	271
945	495.8098	560.9156	400.4304	274.5704	640	512	276	279
990	495.4048	566.1851	400.9915	277.118	640	512	306	289

It shows phase corellations for 180 degree differences in orientation, although the standard deviations are significantly larger than expected. However, the expected circular motion does not materialize, with the responses remaining consistent only over short curves which - while they comprise the bulk of the trial data - are less than a full turn in length.

IMPORTANT: Data Analysis for trial 4 has been revised due to a computational error.

My initial analysis of the data for trial 4 was flawed by a bug in the program I was using for the analysis computations. I am leaving the results of the initial analysis posted, but the new results are dramatically different.

The nature of the error was that I was directing the program to perform its analysis using an arc of the surrounding interference pattern rather than the central peak of the image. This problem showed up most clearly in the median and modal data, which was not corresponding to the actual image center or widest point.

The resulting data set is significantly cleaner, with a much smaller standard deviation of width and height. The mode and median also reflect the image position more accurately.

The trial was not repeated, as this was a mistake of the analysis, and does not affect the original image data.

The revised results are as follows:

		MEAN			STDEV		MEDIAN		MODE
ANGLE	MEASURE	X	Xadj	Y	X	Y	X	Y	X	Y
270	270	682.9644	1.0324	338.3343	90.31181	115.3201	691	346	450	349
315	315	685.0413	2.2723	337.5316	90.26759	114.5085	696	342	446	344
360	0	684.7097	1.1037	337.9933	90.20683	114.761	695	342	447	344
405	45	684.4147	-0.0283	339.1512	89.04697	112.7176	693	350	436	347
450	90	685.0779	-0.2021	337.0707	89.25467	112.6961	696	342	440	344
495	135	684.6427	-1.4743	337.8658	89.06789	114.8095	695	344	448	338
540	180	685.5358	-1.4182	338.3359	89.16213	111.5343	695	344	432	344
585	225	685.4281	-2.3629	337.2373	88.71008	114.3524	694	346	443	342
630	270	686.2203	-2.4077	335.3727	88.71331	114.6049	695	344	445	342
675	315	687.3045	-2.1605	338.5482	88.49126	114.3669	696	346	444	339
720	0	690.6735	0.3715	339.6088	88.47781	114.3491	699	344	445	335
765	45	693.4189	2.2799	340.3135	89.0443	110.8157	701	346	427	344
810	90	692.6639	0.6879	339.3615	88.52756	114.406	700	347	442	342
855	135	693.6422	0.8292	336.7235	88.06847	114.5355	700	345	443	337
900	180	694.1811	0.5311	336.2569	88.77237	112.5172	700	348	435	346
945	225	695.1663	0.6793	333.2405	88.92583	111.2358	702	338	426	339
990	270	695.2379	-0.0861	332.3148	88.16959	113.5854	702	335	440	333

A computed value of the x-coordinate computed relative to the linear fit for the mean x-coordinate data is added. The equation of this linear fit is x = 676.91 + 0.0186α. The purpose of this computation is to explore the possibility of correction versus drift.

(11-24-07)

After coordinating a simultaneous controlled trial with Dr. Lance Osadchey, I recognized a computational error in my adjusted data. I have changed the angle scale assigned so that 0 deg = North, and changed the data fit used to compute the adjusted coordinates.

Trial 4
5/27/07,End at 16:28:00, 15 second interval
08:56:04 Sidereal Time
MEAN STDEV MEDIAN MODE
ANGLE MEASURE X Xadj Y Yadj X Y X Y X Y
180 180 682.9644 -0.5336 338.3343 -1.1883 90.31181 115.3201 691 346 450 349
225 225 685.0413 1.2688 337.5316 0.2084 90.26759 114.5085 696 342 446 344
270 270 684.7097 0.5817 337.9933 0.2597 90.20683 114.761 695 342 447 344
315 315 684.4147 -0.1498 339.1512 -0.4662 89.04697 112.7176 693 350 436 347
360 0 685.0779 -0.0041 337.0707 1.9653 89.25467 112.6961 696 342 440 344
405 45 684.6427 -1.0378 337.8658 1.4402 89.06789 114.8095 695 344 448 338
450 90 685.5358 -0.8242 338.3359 1.1591 89.16213 111.5343 695 344 432 344
495 135 685.4281 -1.6924 337.2373 2.3657 88.71008 114.3524 694 346 443 342
540 180 686.2203 -1.7417 335.3727 4.2573 88.71331 114.6049 695 344 445 342
585 225 687.3045 -1.58 338.5482 1.0278 88.49126 114.3669 696 346 444 339
630 270 690.6735 0.7855 339.6088 -0.1678 88.47781 114.3491 699 344 445 335
675 315 693.4189 2.4464 340.3135 -1.0885 89.0443 110.8157 701 346 427 344
720 0 692.6639 0.5259 339.3615 -0.4335 88.52756 114.406 700 347 442 342
765 45 693.6422 0.2577 336.7235 1.8265 88.06847 114.5355 700 345 443 337
810 90 694.1811 -0.5309 336.2569 1.8341 88.77237 112.5172 700 348 435 346
855 135 695.1663 -0.9542 333.2405 4.3105 88.92583 111.2358 702 338 426 339
900 180 695.2379 -2.3721 332.3148 4.6152 88.16959 113.5854 702 335 440 333
Angles have been reassigned to reflect 0 deg = north.
The adjusted data are determined using a second order polynomial fit as an approximation for drift vs. angle.
X Y
a 2.00E-05 -2.00E-05
b -0.002 0.0213
c 683.21 333.96
The adjusted data have been altered to show position of incidence as seen through the laser aperture
instead of relative to the photographs.
Averages
X Y
0 0.2609 0.7659
45 -0.39005 1.63335
90 -0.67755 1.4966
135 -1.3233 3.3381
180 -2.0569 4.43625
225 -1.3233 3.3381
270 -1.5491333 2.5614
315 -0.1556 0.6181
Estimated Max X 180 deg
Estimated Magnitude 4.466594 pixels 17.86638 microns

These are a chart of the calculated mean positions and a chart of the calculated mean coordinates graphed independently. The actual image motion is subject to substantial drift, which is approximately linear with an approximately sinusoidal motion superimposed on that. However, after adjusting for drift, the motion is at the limit of the expected range predicted by Dr. Osadchey's results. Also, the period of the adjusted motion does not directly correspond to the motion of the apparatus.

Trial 4
5/27/07,End at 16:28:00, 15 second interval
08:56:04 Sidereal Time

		MEAN				STDEV		MEDIAN		MODE
ANGLE	MEASURE	X	Xadj	Y	Yadj	X	Y	X	Y	X	Y
180	180	682.9644	-0.5336	338.3343	-1.1883	90.31181	115.3201	691	346	450	349
225	225	685.0413	1.2688	337.5316	0.2084	90.26759	114.5085	696	342	446	344
270	270	684.7097	0.5817	337.9933	0.2597	90.20683	114.761	695	342	447	344
315	315	684.4147	-0.1498	339.1512	-0.4662	89.04697	112.7176	693	350	436	347
360	0	685.0779	-0.0041	337.0707	1.9653	89.25467	112.6961	696	342	440	344
405	45	684.6427	-1.0378	337.8658	1.4402	89.06789	114.8095	695	344	448	338
450	90	685.5358	-0.8242	338.3359	1.1591	89.16213	111.5343	695	344	432	344
495	135	685.4281	-1.6924	337.2373	2.3657	88.71008	114.3524	694	346	443	342
540	180	686.2203	-1.7417	335.3727	4.2573	88.71331	114.6049	695	344	445	342
585	225	687.3045	-1.58	338.5482	1.0278	88.49126	114.3669	696	346	444	339
630	270	690.6735	0.7855	339.6088	-0.1678	88.47781	114.3491	699	344	445	335
675	315	693.4189	2.4464	340.3135	-1.0885	89.0443	110.8157	701	346	427	344
720	0	692.6639	0.5259	339.3615	-0.4335	88.52756	114.406	700	347	442	342
765	45	693.6422	0.2577	336.7235	1.8265	88.06847	114.5355	700	345	443	337
810	90	694.1811	-0.5309	336.2569	1.8341	88.77237	112.5172	700	348	435	346
855	135	695.1663	-0.9542	333.2405	4.3105	88.92583	111.2358	702	338	426	339
900	180	695.2379	-2.3721	332.3148	4.6152	88.16959	113.5854	702	335	440	333

Angles have been reassigned to reflect 0 deg = north.
The adjusted data are determined using a second order polynomial fit as an approximation for drift vs. angle.

	X	Y
a	2.00E-05	-2.00E-05
b	-0.002	0.0213
c	683.21	333.96

The adjusted data have been altered to show position of incidence as seen through the laser aperture
instead of relative to the photographs.

Averages
	X	Y
0	0.2609	0.7659
45	-0.39005	1.63335
90	-0.67755	1.4966
135	-1.3233	3.3381
180	-2.0569	4.43625
225	-1.3233	3.3381
270	-1.5491333	2.5614
315	-0.1556	0.6181

Estimated Max X		180	deg
Estimated Magnitude		4.466594	pixels	17.86638	microns