[note: click on any figure to see it full size]

Completeness

For the completeness analysis objects in the truth list were searched for in the coadd detected source list using a 1 arcsec search radius. No SNR, blending flag, or upper limit cuts were made to the coadd detected source list in this analysis. The completeness is defined as the ratio of the ratio of truth sources that matched MDEX sources to the total number of truth sources (N_{Truth-MDEX matches}/N_{Total truth}).

The first set of images shows the flux-binned completeness (top row) and total number of matches (bottom row) as a function of the truth flux. There is very little difference between the simulations with and without the pattern noise.

These plots show the cumulative completeness and match totals as a function of truth flux. While the results between the no noise pattern and noise pattern simulations are similar, there does appear to be a subtle increase in the total number of matches in the simulation with the noise pattern.

Reliability

The reliability was determined by taking the ratio of the coadd sources matched to truth sources to the total number of coadd sources (N_{MDEX-Truth matches}/N_{total MDEX sources}). A search radius of 1 arcsec was used. The MDEX source list was cut according to the following parameters:

profile magnitude error <9.98 (w[1-4]sigmpro < 9.98)
standard aperture error <9.98 (w[1-4]sigm < 9.98)
number of deblended components = 1 (nb=1)
source not actively deblended (na=0)

The first two cuts ensure that the presented magnitudes are not upper limits; the second cuts make sure the sources are isolated singles.

There are subtle differences in the reliabilities between the two simulations. The differences for the brightest sources and faintest sources are due to small number statistics (see the tables below).

The following sets of plots show the cumulative reliability summed up from faint to bright sources.
W4 is most impacted by the noise pattern in this simulation. The overall reliability drops by approximately 2% with the noise.
W3 shows an unexpected increase in the reliability relative to the no pattern noise set of images. While there are fewer total sources that are detected, a larger fraction of them are being matched with objects in the truth list. This is most important for sources fainter than about mag=10. The most likely cause is that we are finding more chance matches in the noise pattern sim than in the no pattern noise sim. This will be investigated in the future.

Reliability output for W1
No Pattern Noise With Pattern Noise

Mag bin matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.) matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.)

19.200 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

18.700 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

18.200 0 3 0.000 0 3 0.000 0 5 0.000 0 5 0.000

17.700 6 149 0.040 6 152 0.039 7 153 0.046 7 158 0.044

17.200 177 630 0.281 183 782 0.234 141 579 0.244 148 737 0.201

16.700 3122 5216 0.599 3305 5998 0.551 3183 5217 0.610 3331 5954 0.559

16.200 10672 15619 0.683 13977 21617 0.647 10630 15596 0.682 13961 21550 0.648

15.700 13574 20007 0.678 27551 41624 0.662 13571 20091 0.675 27532 41641 0.661

15.200 8219 11822 0.695 35770 53446 0.669 8290 11811 0.702 35822 53452 0.670

14.700 5022 7232 0.694 40792 60678 0.672 4792 7023 0.682 40614 60475 0.672

14.200 2934 4187 0.701 43726 64865 0.674 2963 4208 0.704 43577 64683 0.674

13.700 1779 2343 0.759 45505 67208 0.677 1725 2271 0.760 45302 66954 0.677

13.200 959 1104 0.869 46464 68312 0.680 956 1093 0.875 46258 68047 0.680

12.700 564 623 0.905 47028 68935 0.682 588 637 0.923 46846 68684 0.682

12.200 382 410 0.932 47410 69345 0.684 386 404 0.955 47232 69088 0.684

11.700 259 264 0.981 47669 69609 0.685 251 257 0.977 47483 69345 0.685

11.200 138 144 0.958 47807 69753 0.685 137 141 0.972 47620 69486 0.685

10.700 67 67 1.000 47874 69820 0.686 69 69 1.000 47689 69555 0.686

10.200 54 54 1.000 47928 69874 0.686 49 49 1.000 47738 69604 0.686

9.700 49 49 1.000 47977 69923 0.686 50 51 0.980 47788 69655 0.686

9.200 27 27 1.000 48004 69950 0.686 24 24 1.000 47812 69679 0.686

8.700 22 22 1.000 48026 69972 0.686 24 24 1.000 47836 69703 0.686

8.200 16 16 1.000 48042 69988 0.686 18 18 1.000 47854 69721 0.686

7.700 19 19 1.000 48061 70007 0.687 14 15 0.933 47868 69736 0.686

7.200 12 12 1.000 48073 70019 0.687 6 7 0.857 47874 69743 0.686

6.700 8 8 1.000 48081 70027 0.687 6 6 1.000 47880 69749 0.686

6.200 2 2 1.000 48083 70029 0.687 5 5 1.000 47885 69754 0.686

5.700 7 7 1.000 48090 70036 0.687 4 4 1.000 47889 69758 0.687

*Reliability output for W1*
	No Pattern Noise	With Pattern Noise
Mag bin	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)
19.200	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
18.700	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
18.200	0	3	0.000	0	3	0.000	0	5	0.000	0	5	0.000
17.700	6	149	0.040	6	152	0.039	7	153	0.046	7	158	0.044
17.200	177	630	0.281	183	782	0.234	141	579	0.244	148	737	0.201
16.700	3122	5216	0.599	3305	5998	0.551	3183	5217	0.610	3331	5954	0.559
16.200	10672	15619	0.683	13977	21617	0.647	10630	15596	0.682	13961	21550	0.648
15.700	13574	20007	0.678	27551	41624	0.662	13571	20091	0.675	27532	41641	0.661
15.200	8219	11822	0.695	35770	53446	0.669	8290	11811	0.702	35822	53452	0.670
14.700	5022	7232	0.694	40792	60678	0.672	4792	7023	0.682	40614	60475	0.672
14.200	2934	4187	0.701	43726	64865	0.674	2963	4208	0.704	43577	64683	0.674
13.700	1779	2343	0.759	45505	67208	0.677	1725	2271	0.760	45302	66954	0.677
13.200	959	1104	0.869	46464	68312	0.680	956	1093	0.875	46258	68047	0.680
12.700	564	623	0.905	47028	68935	0.682	588	637	0.923	46846	68684	0.682
12.200	382	410	0.932	47410	69345	0.684	386	404	0.955	47232	69088	0.684
11.700	259	264	0.981	47669	69609	0.685	251	257	0.977	47483	69345	0.685
11.200	138	144	0.958	47807	69753	0.685	137	141	0.972	47620	69486	0.685
10.700	67	67	1.000	47874	69820	0.686	69	69	1.000	47689	69555	0.686
10.200	54	54	1.000	47928	69874	0.686	49	49	1.000	47738	69604	0.686
9.700	49	49	1.000	47977	69923	0.686	50	51	0.980	47788	69655	0.686
9.200	27	27	1.000	48004	69950	0.686	24	24	1.000	47812	69679	0.686
8.700	22	22	1.000	48026	69972	0.686	24	24	1.000	47836	69703	0.686
8.200	16	16	1.000	48042	69988	0.686	18	18	1.000	47854	69721	0.686
7.700	19	19	1.000	48061	70007	0.687	14	15	0.933	47868	69736	0.686
7.200	12	12	1.000	48073	70019	0.687	6	7	0.857	47874	69743	0.686
6.700	8	8	1.000	48081	70027	0.687	6	6	1.000	47880	69749	0.686
6.200	2	2	1.000	48083	70029	0.687	5	5	1.000	47885	69754	0.686
5.700	7	7	1.000	48090	70036	0.687	4	4	1.000	47889	69758	0.687

Reliability output for W2
No Pattern Noise With Pattern Noise

Mag bin matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.) matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.)

19.200 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

18.700 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

18.200 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

17.700 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

17.200 3 12 0.250 3 12 0.250 5 12 0.417 5 12 0.417

16.700 155 385 0.403 158 397 0.398 163 390 0.418 168 402 0.418

16.200 1027 1762 0.583 1185 2159 0.549 1111 1886 0.589 1279 2288 0.559

15.700 4586 7262 0.632 5771 9421 0.613 4534 7169 0.632 5813 9457 0.615

15.200 8793 13828 0.636 14564 23249 0.626 8772 13722 0.639 14585 23179 0.629

14.700 7010 10644 0.659 21574 33893 0.637 6806 10437 0.652 21391 33616 0.636

14.200 5046 7501 0.673 26620 41394 0.643 4935 7450 0.662 26326 41066 0.641

13.700 3045 4397 0.693 29665 45791 0.648 3072 4392 0.699 29398 45458 0.647

13.200 1552 1969 0.788 31217 47760 0.654 1520 1897 0.801 30918 47355 0.653

12.700 721 822 0.877 31938 48582 0.657 763 849 0.899 31681 48204 0.657

12.200 436 462 0.944 32374 49044 0.660 448 475 0.943 32129 48679 0.660

11.700 279 290 0.962 32653 49334 0.662 272 279 0.975 32401 48958 0.662

11.200 171 178 0.961 32824 49512 0.663 161 168 0.958 32562 49126 0.663

10.700 72 76 0.947 32896 49588 0.663 80 81 0.988 32642 49207 0.663

10.200 67 68 0.985 32963 49656 0.664 57 57 1.000 32699 49264 0.664

9.700 46 46 1.000 33009 49702 0.664 44 45 0.978 32743 49309 0.664

9.200 33 33 1.000 33042 49735 0.664 34 34 1.000 32777 49343 0.664

8.700 20 20 1.000 33062 49755 0.664 22 22 1.000 32799 49365 0.664

8.200 21 21 1.000 33083 49776 0.665 22 22 1.000 32821 49387 0.665

7.700 17 17 1.000 33100 49793 0.665 13 14 0.929 32834 49401 0.665

7.200 14 14 1.000 33114 49807 0.665 8 9 0.889 32842 49410 0.665

6.700 7 7 1.000 33121 49814 0.665 6 6 1.000 32848 49416 0.665

6.200 3 3 1.000 33124 49817 0.665 3 3 1.000 32851 49419 0.665

5.700 8 8 1.000 33132 49825 0.665 6 6 1.000 32857 49425 0.665

*Reliability output for W2*
	No Pattern Noise	With Pattern Noise
Mag bin	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)
19.200	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
18.700	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
18.200	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
17.700	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
17.200	3	12	0.250	3	12	0.250	5	12	0.417	5	12	0.417
16.700	155	385	0.403	158	397	0.398	163	390	0.418	168	402	0.418
16.200	1027	1762	0.583	1185	2159	0.549	1111	1886	0.589	1279	2288	0.559
15.700	4586	7262	0.632	5771	9421	0.613	4534	7169	0.632	5813	9457	0.615
15.200	8793	13828	0.636	14564	23249	0.626	8772	13722	0.639	14585	23179	0.629
14.700	7010	10644	0.659	21574	33893	0.637	6806	10437	0.652	21391	33616	0.636
14.200	5046	7501	0.673	26620	41394	0.643	4935	7450	0.662	26326	41066	0.641
13.700	3045	4397	0.693	29665	45791	0.648	3072	4392	0.699	29398	45458	0.647
13.200	1552	1969	0.788	31217	47760	0.654	1520	1897	0.801	30918	47355	0.653
12.700	721	822	0.877	31938	48582	0.657	763	849	0.899	31681	48204	0.657
12.200	436	462	0.944	32374	49044	0.660	448	475	0.943	32129	48679	0.660
11.700	279	290	0.962	32653	49334	0.662	272	279	0.975	32401	48958	0.662
11.200	171	178	0.961	32824	49512	0.663	161	168	0.958	32562	49126	0.663
10.700	72	76	0.947	32896	49588	0.663	80	81	0.988	32642	49207	0.663
10.200	67	68	0.985	32963	49656	0.664	57	57	1.000	32699	49264	0.664
9.700	46	46	1.000	33009	49702	0.664	44	45	0.978	32743	49309	0.664
9.200	33	33	1.000	33042	49735	0.664	34	34	1.000	32777	49343	0.664
8.700	20	20	1.000	33062	49755	0.664	22	22	1.000	32799	49365	0.664
8.200	21	21	1.000	33083	49776	0.665	22	22	1.000	32821	49387	0.665
7.700	17	17	1.000	33100	49793	0.665	13	14	0.929	32834	49401	0.665
7.200	14	14	1.000	33114	49807	0.665	8	9	0.889	32842	49410	0.665
6.700	7	7	1.000	33121	49814	0.665	6	6	1.000	32848	49416	0.665
6.200	3	3	1.000	33124	49817	0.665	3	3	1.000	32851	49419	0.665
5.700	8	8	1.000	33132	49825	0.665	6	6	1.000	32857	49425	0.665

Reliability output for W3
No Pattern Noise With Pattern Noise

Mag bin matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.) matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.)

13.500 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

13.000 2 4 0.500 2 4 0.500 0 1 0.000 0 1 0.000

12.500 179 343 0.522 181 347 0.522 177 311 0.569 177 312 0.567

12.000 489 885 0.553 670 1232 0.544 435 847 0.514 612 1159 0.528

11.500 794 1272 0.624 1464 2504 0.585 757 1194 0.634 1369 2353 0.582

11.000 700 942 0.743 2164 3446 0.628 695 928 0.749 2064 3281 0.629

10.500 322 375 0.859 2486 3821 0.651 337 387 0.871 2401 3668 0.655

10.000 143 152 0.941 2629 3973 0.662 141 152 0.928 2542 3820 0.665

9.500 93 94 0.989 2722 4067 0.669 91 94 0.968 2633 3914 0.673

9.000 48 48 1.000 2770 4115 0.673 48 48 1.000 2681 3962 0.677

8.500 31 33 0.939 2801 4148 0.675 28 29 0.966 2709 3991 0.679

8.000 19 19 1.000 2820 4167 0.677 18 18 1.000 2727 4009 0.680

7.500 16 16 1.000 2836 4183 0.678 12 13 0.923 2739 4022 0.681

7.000 14 14 1.000 2850 4197 0.679 11 12 0.917 2750 4034 0.682

6.500 4 4 1.000 2854 4201 0.679 3 3 1.000 2753 4037 0.682

6.000 2 2 1.000 2856 4203 0.680 2 2 1.000 2755 4039 0.682

5.500 8 8 1.000 2864 4211 0.680 7 7 1.000 2762 4046 0.683

5.000 0 0 -NaN 2864 4211 0.680 0 0 -NaN 2762 4046 0.683

*Reliability output for W3*
	No Pattern Noise	With Pattern Noise
Mag bin	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)
13.500	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
13.000	2	4	0.500	2	4	0.500	0	1	0.000	0	1	0.000
12.500	179	343	0.522	181	347	0.522	177	311	0.569	177	312	0.567
12.000	489	885	0.553	670	1232	0.544	435	847	0.514	612	1159	0.528
11.500	794	1272	0.624	1464	2504	0.585	757	1194	0.634	1369	2353	0.582
11.000	700	942	0.743	2164	3446	0.628	695	928	0.749	2064	3281	0.629
10.500	322	375	0.859	2486	3821	0.651	337	387	0.871	2401	3668	0.655
10.000	143	152	0.941	2629	3973	0.662	141	152	0.928	2542	3820	0.665
9.500	93	94	0.989	2722	4067	0.669	91	94	0.968	2633	3914	0.673
9.000	48	48	1.000	2770	4115	0.673	48	48	1.000	2681	3962	0.677
8.500	31	33	0.939	2801	4148	0.675	28	29	0.966	2709	3991	0.679
8.000	19	19	1.000	2820	4167	0.677	18	18	1.000	2727	4009	0.680
7.500	16	16	1.000	2836	4183	0.678	12	13	0.923	2739	4022	0.681
7.000	14	14	1.000	2850	4197	0.679	11	12	0.917	2750	4034	0.682
6.500	4	4	1.000	2854	4201	0.679	3	3	1.000	2753	4037	0.682
6.000	2	2	1.000	2856	4203	0.680	2	2	1.000	2755	4039	0.682
5.500	8	8	1.000	2864	4211	0.680	7	7	1.000	2762	4046	0.683
5.000	0	0	-NaN	2864	4211	0.680	0	0	-NaN	2762	4046	0.683

Reliability output for W4
No Pattern Noise With Pattern Noise

Mag bin matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.) matches total sources ratio matches
(cumul.) total sources
(cumul.) ratio
(cumul.)

11.000 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

10.500 0 0 -NaN 0 0 -NaN 0 0 -NaN 0 0 -NaN

10.000 16 41 0.390 16 41 0.390 23 48 0.479 23 48 0.479

9.500 146 305 0.479 162 346 0.468 140 317 0.442 163 365 0.447

9.000 195 392 0.497 357 738 0.484 188 398 0.472 351 763 0.460

8.500 233 407 0.572 590 1145 0.515 232 389 0.596 583 1152 0.506

8.000 208 320 0.650 798 1465 0.545 195 292 0.668 778 1444 0.539

7.500 108 129 0.837 906 1594 0.568 104 127 0.819 882 1571 0.561

7.000 43 44 0.977 949 1638 0.579 32 34 0.941 914 1605 0.569

6.500 17 18 0.944 966 1656 0.583 14 15 0.933 928 1620 0.573

6.000 4 4 1.000 970 1660 0.584 3 3 1.000 931 1623 0.574

5.500 9 9 1.000 979 1669 0.587 8 8 1.000 939 1631 0.576

5.000 4 4 1.000 983 1673 0.588 5 5 1.000 944 1636 0.577

*Reliability output for W4*
	No Pattern Noise	With Pattern Noise
Mag bin	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)	matches	total sources	ratio	matches (cumul.)	total sources (cumul.)	ratio (cumul.)
11.000	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
10.500	0	0	-NaN	0	0	-NaN	0	0	-NaN	0	0	-NaN
10.000	16	41	0.390	16	41	0.390	23	48	0.479	23	48	0.479
9.500	146	305	0.479	162	346	0.468	140	317	0.442	163	365	0.447
9.000	195	392	0.497	357	738	0.484	188	398	0.472	351	763	0.460
8.500	233	407	0.572	590	1145	0.515	232	389	0.596	583	1152	0.506
8.000	208	320	0.650	798	1465	0.545	195	292	0.668	778	1444	0.539
7.500	108	129	0.837	906	1594	0.568	104	127	0.819	882	1571	0.561
7.000	43	44	0.977	949	1638	0.579	32	34	0.941	914	1605	0.569
6.500	17	18	0.944	966	1656	0.583	14	15	0.933	928	1620	0.573
6.000	4	4	1.000	970	1660	0.584	3	3	1.000	931	1623	0.574
5.500	9	9	1.000	979	1669	0.587	8	8	1.000	939	1631	0.576
5.000	4	4	1.000	983	1673	0.588	5	5	1.000	944	1636	0.577

This analysis is a joint effort by Chris Gelino and Sergio Fajardo-Acosta. Chris headed the Reliability analysis and Sergio headed the Completeness analysis.
27 June 2009