TO: 2MASS Team March 3, 1998

FROM: C. Beichman

SUBJECT: Diffraction Spikes Analysis

1. Introduction

I have analyzed images and source lists from a variety of 2MAPPS 1.x and 2.0 data to determine the parameters needed by MAPCOR to eliminate diffraction spike sources. A band-by-band analysis is given below. In general then E/W spikes are broader and more structured than the N/S spikes. This is due to 1) the fact that the E/W vanes on the telescope appear not to be parallel resulting in non-degenerate spikes in this direction; 2) electronic bleeding in the cross-scan direction due to bright sources. This bleeding is sufficiently diffuse that it does not appear to produce a significant number of point sources. I am continuing to analyze these electronic stripes. This memo concentrates on diffraction spikes.

1. K Band Diffraction

Figure 1. Diffraction Spike Sources. K=3.5-6.5

The effects of diffraction spikes are obvious in both the image and point source data. I have analyzed ~20 bright sources to ensure the correct operation of the spike-flagging software and to refine the parameters. In setting the parameters, I have erred on the side of reliability in the catalog entries.

Figure 1 shows all the sources tagged as diffraction spikes for sources covering a range of magnitudes from K=3.5 to K=6.5 mag. These sources were examined visually to verify that these are ALL the sources extracted in the vicinity of the diffraction spikes. I removed a few glints at 11:30 and 5:30 o'clock, as well as a few sources that were obviously real stars within the nominal spike window.

There are a number of patterns obvious from visual inspection of the images. The distribution of the diffraction sources around the centerline of the spikes is remarkably narrow with a population sigma of 0.4 arcsec. The Western spike is more complex than the other three spikes and appears to consist of two spikes that flare with increasing distance from the parent star. The most noticeable effect of this structure is that the Western spike is 2-3 times broader than the N, S, or E spikes. Based on the appearance of the images and the derived source data, I adopt a conservative strategy of making the E/W exclusion zones equal to each other and three times larger than the N/S zones. Another effect apparent in the data is that because the diffracted energy is divided between the two rays, diffraction sources fall below threshold more rapidly with distance than for the other spikes. This is a 10-20 % effect in the relative lengths of the East and West spikes. In the interests of adopting very conservative criteria, I have not decreased the length of the exclusion zone for the E/W spikes due to this effect.

Figure 2. Length of diffraction spike as a function of source brightness (K band).

The derived K-band values for the diffraction spike parameters are listed below. Since excising diffraction spike sources is an important reliability consideration, the length proposed for MAPCOR is 20% larger than the observed values. This length is parameterized according to Length(K)=Length0*10^(-slope*(K-6 mag)). The values in Table 1 were derived by examining the length of the spikes in 4 separate magnitude bins (Figure 2). The width of the exclusion zone is derived from the absolute value of any offset between the parent star and the spike source, plus 5*sigma_pop. The half width and length of the box are given in units of camera pixels (2") for each cardinal direction.

The spike sources fade slowly with distance from the parent star until they drop below the detection threshold. As shown in Figure 3, the magnitude difference between the parent star and spike sources declines by about 1.1 mag as the distance increases from 10 to 100 arcseconds. The equation fitted to the data in Figure 3 is given by DeltaMag =1.1*log(Radius)+8.4. MAPCOR presently cannot use the variation. I adopt a constant difference in magnitude between the parent and diffraction sources, DeltaMag = 10.2+/-0.6 mag which I used in two ways:

• Since the 3-sigma K detection threshold is K~15.6 mag, then to guarantee that no spike sources escape flagging, one must search around sources as faint as K=15.6- DeltaMag +5*sigma_pop= 8.4 mag. If the parent drops below this magnitude, no more spike sources should be detectable. Accordingly, we have added a diffrac_cutoff = 8.5 mag to MAPCOR, below which there is no need to search for diffraction spikes.
• Sources which are 5*sigma_pop times brighter than the predicted spike brightness, Kparent + DeltaMag - 5*sigma_pop = Kparent + 7.2 mag, are probably real sources, albeit ones contaminated by the spike. These will be marked with the diff1 contamination flag.

Figure 3. Brightness of diffraction spike sources as function of distance from parent source (K band).

Table 1. Properties of Diffraction Spikes at K
	North	South	East	West
Box Half Width (camera pixel, 2")	0.5	0.5	1.5	1.5
Box Length at K=6 mag (camera pixel, 2")	15	15	15	15
Max length (camera pixel, 2")	50	50	50	50
Slope	-0.22
diffrac_cutoff	K= 8.5 mag
Contamination threshold	Kparent + 7.2 mag

II. H Band Diffraction

The spike parameters for H band are given in Table 2. The width of the E/W spikes is greater than the N/S spikes, consistent with the K band. However, the slope of the magnitude dependence of the spike length is shallower at H than at K (Figure 4). Figure 5 shows a fit to the falloff with radius for sources in the range H= 5-5.5 given by DeltaMag(radius) = 1.93 * log(radius) + 7.2. However, I have used a constant DeltaMag=10.1+/-0.7 mag to derive the cutoff brightness for searching for diffraction artifacts.

Figure 4. Length of diffraction spike as a function of source brightness (H band).

• Since the 3-sigma H detection threshold is H~16.4 mag, then to guarantee that no spike sources escape flagging, one must search around sources as faint as H=16.4- DeltaMag +5*sigma_pop~ 9.8 mag. If the parent drops below this magnitude, no more spike sources should be detectable. Accordingly, we have added a diffrac_cutoff = 9.8 mag to MAPCOR, below which there is no need to search for diffraction spikes.
• Sources which are 5*sigma_pop times brighter than the predicted spike brightness, Hparent + DeltaMag - 5*sigma_pop = Hparent + 6.6 mag, are probably real sources, albeit ones contaminated by the spike. These will be marked with the diff1 contamination flag.
  
  

Figure 5. Brightness of diffraction spike sources as function of distance from parent source (H band).

Table 2. Properties of Diffraction Spikes at H
	North	South	East	West
Box Half Width (camera pixel, 2")	0.9	0.9	1.5	1.5
Box Length at H=6 mag (camera pixel, 2")	26	26	26	26
Max length (camera pixel, 2")	50	50	50	50
Slope	-0.12
diffrac_cutoff	H= 9.8 mag
Contamination threshold	Hparent + 6.6 mag

1. J Band Diffraction

The J band data for sources in the J=4-5 mag range show a steeper falloff of spike source brightness with radius than at the longer wavelengths (Figure 6), consistent with the diffraction nature of the effect. The fit to the observations is DeltaMag(radius) =6.3*log(Radius) - 0.67. As a result of this more pronounced dependence, the calculated constant DeltaMag and its dispersion are larger than at other wavelengths. In future releases of 2MAPPS it might be appropriate to build in a radial falloff in spike brightness rather than a simple exclusion box for flagging sources. For the purposes of this analysis, I adopt conservative limits on DeltaMag = 10.0+/-1.0 mag.

• Since the 3-sigma J detection threshold is J~17 mag, then to guarantee that no spike sources escape flagging, one must search around sources as faint as J=17- DeltaMag +5*sigma_pop= 12 mag. If the parent drops below this magnitude, no more spike sources should be detectable. Accordingly, we have added a diffrac_cutoff = 12 mag to MAPCOR, below which there is no need to search for diffraction spikes.

Figure 6. Brightness of diffraction spike sources as function of distance from parent source (J band).

• Sources which are 5*sigma_pop times brighter than the predicted spike brightness, Jparent + DeltaMag - 5*sigma_pop = Jparent + 5 mag, are probably real sources, albeit ones contaminated by the spike. These will be marked with the diff1 contamination flag.

Table 2. Properties of Diffraction Spikes at J
	North	South	East	West
Box Half Width (camera pixel, 2")	0.6	0.6	1.5	1.5
Box Length at J=6 mag (camera pixel, 2")	20	20	20	20
Max length (camera pixel, 2")	50	50	50	50
Slope	-0.16
diffrac_cutoff	J= 12 mag
Contamination threshold	Jparent + 5 mag

The length of the diffraction spike varies with J-band brightness with a slope of -0.16, similar to the other bands, but with a smaller overall length, consistent with the diffraction nature of the effect.

Figure 7. Length of diffraction spike as a function of source brightness (J band).