Table 1.

Results of maximum likelihood estimations

Data set no.	Imaging modality	Axial position sz (nm)	Orientation angle ω (degrees)	Distance of separation d (nm)	Mean of d estimates (nm)	Resolution measure (nm)	Standard deviation of d estimates (nm)
1	SIM-SNG	400	60	200	201.09	13.71	13.93
2	SEP-SNG	400	60	200	200.60	7.82	7.91
3	SIM-MUM	400	60	200	201.43	12.09	12.10
4	SEP-MUM	400	60	200	200.81	9.59	9.53
5	SEP-SNG	400	30	100	99.95	11.12	11.29
6	SEP-MUM	400	30	100	100.38	15.47	15.49
7	SIM-MUM	75	60	200	200.65	12.29	12.03
8	SEP-MUM	75	60	200	200.63	9.58	9.66
9	SEP-MUM	75	30	100	100.44	15.54	15.85

Results of maximum likelihood estimations on nine sets of simulated images of point source pairs in 3D space. The image of each point source is simulated according to the Born and Wolf 3D point spread function, and the expected photon count detected per point source is 5000. For each data set, the mean and the standard deviation of 500 estimates of the distance of separation are shown with the corresponding resolution measure as well as the axial position s_z, the orientation angle ω, and the distance of separation d which are different between the data sets. The data sets also differ in terms of the imaging modality. A data set corresponding to the SIM-SNG modality contains 500 simulated images. A data set corresponding to the SEP-SNG or the SIM-MUM modality contains 500 pairs of simulated images. A data set corresponding to the SEP-MUM modality contains 500 sets of four images. (See Fig. 1.) In all data sets, a single image is a 15×15 array of 13 μm by 13 μm pixels. With an assumed magnification of M = 100, the position of the point source pair in the xy-plane is set to s_x = s_y = 975 nm so that its image is centered on the pixel array. All other experimental, noise, and point source pair parameters are as given in Fig. 3.