Preface |
|
ix | |
Acknowledgments |
|
xi | |
|
|
1 | (40) |
|
|
3 | (2) |
|
|
5 | (2) |
|
2 Introduction to Two Problems in Cellular Biology |
|
|
7 | (10) |
|
|
7 | (2) |
|
2.2 Localization experiments |
|
|
9 | (1) |
|
2.3 Association experiments |
|
|
9 | (3) |
|
|
12 | (1) |
|
2.5 Iron transport, transferrin, and the transferrin receptor |
|
|
13 | (4) |
|
3 Basics of Microscopy Techniques |
|
|
17 | (12) |
|
3.1 Optical microscopy for cell biology |
|
|
17 | (1) |
|
3.2 Transmitted light microscopy |
|
|
17 | (1) |
|
3.3 Fluorescence microscopy |
|
|
18 | (4) |
|
|
20 | (1) |
|
3.3.2 Layout of an epifluorescence widefield microscope |
|
|
21 | (1) |
|
3.4 Inverted versus upright microscope |
|
|
22 | (1) |
|
3.5 Components of commercial microscopes |
|
|
23 | (4) |
|
|
24 | (2) |
|
|
26 | (1) |
|
3.6 Fixed and live cell experiments |
|
|
27 | (1) |
|
|
27 | (1) |
|
3.8 A note regarding safety |
|
|
28 | (1) |
|
4 Introduction to Image Formation and Analysis |
|
|
29 | (12) |
|
4.1 Image formation and point spread functions |
|
|
29 | (2) |
|
4.2 Resolution: an elementary introduction |
|
|
31 | (3) |
|
4.3 Modeling and analyzing the data |
|
|
34 | (3) |
|
|
37 | (2) |
|
|
39 | (2) |
|
|
41 | (86) |
|
|
43 | (2) |
|
|
45 | (20) |
|
|
45 | (1) |
|
|
46 | (2) |
|
5.3 How are proteins made? |
|
|
48 | (5) |
|
5.4 Structures of proteins |
|
|
53 | (5) |
|
5.5 Protein structure determination |
|
|
58 | (7) |
|
|
65 | (12) |
|
6.1 Structure of antibodies |
|
|
65 | (2) |
|
6.2 Variable regions and binding activity |
|
|
67 | (2) |
|
|
69 | (2) |
|
6.4 Antibody production for laboratory and clinical use |
|
|
71 | (2) |
|
6.4.1 The classical method: hybridoma technology |
|
|
71 | (2) |
|
6.5 Diagnostic techniques using antibody detection methods |
|
|
73 | (4) |
|
6.5.1 Enzyme-linked immunosorbent assay |
|
|
73 | (2) |
|
6.5.2 Surface plasmon resonance for the quantitation of the affinity of an interaction |
|
|
75 | (2) |
|
7 Cloning of genes for protein expression |
|
|
77 | (14) |
|
7.1 Features of expression constructs |
|
|
77 | (1) |
|
7.2 Methods for generating expression plasmids |
|
|
78 | (8) |
|
7.2.1 Restriction enzymes |
|
|
78 | (1) |
|
7.2.2 Polymerase chain reaction |
|
|
79 | (1) |
|
7.2.3 Details of approaches for generating expression plasmids |
|
|
79 | (7) |
|
7.2.4 Transfection of mammalian cells for expression |
|
|
86 | (1) |
|
|
86 | (5) |
|
7.3.1 Chimeric antibodies |
|
|
87 | (1) |
|
7.3.2 Humanized antibodies |
|
|
88 | (1) |
|
7.3.3 Isolation of V regions |
|
|
88 | (3) |
|
8 Principles of Fluorescence |
|
|
91 | (16) |
|
8.1 Wave and particle description of light |
|
|
91 | (1) |
|
|
91 | (1) |
|
|
92 | (1) |
|
|
93 | (1) |
|
8.5 Photophysical characterization of fluorophores |
|
|
94 | (2) |
|
|
94 | (1) |
|
8.5.2 Beer-Lambert law, effective absorption cross section and molar extinction coefficient |
|
|
95 | (1) |
|
8.5.3 Brightness of a fluorophore |
|
|
96 | (1) |
|
8.6 Excitation and emission spectra |
|
|
96 | (1) |
|
|
97 | (10) |
|
8.7.1 Chemical fluorescent dyes |
|
|
97 | (1) |
|
8.7.1.1 Labeling of proteins via cysteine or lysine residues |
|
|
98 | (1) |
|
8.7.1.2 Labeling of proteins with fluorophore-conjugated strepta-vidin |
|
|
98 | (2) |
|
8.7.1.3 In situ labeling of proteins in cells using peptide tags |
|
|
100 | (1) |
|
|
100 | (1) |
|
8.7.2.1 Labeling of proteins with quantum dots |
|
|
101 | (1) |
|
8.7.3 Fluorescent proteins |
|
|
102 | (3) |
|
8.7.4 Photoactivatable and photoswitchable fluorescent probes |
|
|
105 | (1) |
|
8.7.5 Other labeling modalities |
|
|
105 | (2) |
|
|
107 | (20) |
|
|
107 | (4) |
|
|
111 | (1) |
|
9.3 Typical biological systems |
|
|
112 | (1) |
|
9.3.1 Subcellular trafficking of the Fc receptor, FcRn |
|
|
112 | (1) |
|
9.3.2 Subcellular trafficking of the transferrin receptor |
|
|
112 | (1) |
|
|
112 | (9) |
|
9.4.1 Labeling of proteins in fixed cells |
|
|
113 | (1) |
|
9.4.2 Sample preparation for typical fixed cell experiments |
|
|
114 | (1) |
|
9.4.3 Sample preparation for typical live cell imaging experiments |
|
|
115 | (6) |
|
|
121 | (4) |
|
|
125 | (2) |
|
III Optics and Microscopy |
|
|
127 | (136) |
|
|
129 | (2) |
|
|
131 | (24) |
|
10.1 Light path for widefield fluorescence microscopy |
|
|
131 | (1) |
|
10.1.1 Infinity-corrected light path |
|
|
131 | (1) |
|
10.2 Imaging in three dimensions |
|
|
132 | (1) |
|
10.2.1 Focus control and acquisition of z-stacks |
|
|
132 | (1) |
|
10.2.2 Multifocal plane microscopy |
|
|
133 | (1) |
|
10.3 Imaging of multiple colors |
|
|
133 | (2) |
|
10.4 Light path for confocal microscopy |
|
|
135 | (2) |
|
10.5 Two-photon excitation microscopy |
|
|
137 | (3) |
|
|
140 | (2) |
|
10.6.1 Numerical aperture and immersion medium |
|
|
140 | (1) |
|
|
141 | (1) |
|
10.6.3 Transmission efficiency |
|
|
141 | (1) |
|
|
142 | (9) |
|
10.7.1 Example: a filter set for a GFP-labeled protein |
|
|
145 | (2) |
|
10.7.2 Imaging of multiple fluorophores |
|
|
147 | (4) |
|
10.8 Transmitted light microscopy |
|
|
151 | (4) |
|
11 Microscopy Experiments |
|
|
155 | (32) |
|
11.1 Fixed cell experiments |
|
|
155 | (4) |
|
11.1.1 Localization of FcRn |
|
|
155 | (1) |
|
11.1.2 Association experiments with FcRn, EEA1, LAMP1, and transferrin |
|
|
156 | (2) |
|
11.1.3 Pulse-chase verification of fate of mutated IgG |
|
|
158 | (1) |
|
|
159 | (3) |
|
11.2.1 Acquisition of z-stacks |
|
|
160 | (1) |
|
|
160 | (2) |
|
11.3 Live cell experiments |
|
|
162 | (2) |
|
11.3.1 Example: FcRn-mediated IgG trafficking |
|
|
163 | (1) |
|
11.4 Total internal reflection fluorescence microscopy (TIRFM) |
|
|
164 | (3) |
|
11.4.1 Objective-based total internal reflection fluorescence microscopy |
|
|
164 | (3) |
|
11.4.2 Exocytosis imaged by total internal reflection fluorescence microscopy |
|
|
167 | (1) |
|
11.5 pH measurement and ratiometric imaging |
|
|
167 | (3) |
|
11.6 Single molecule microscopy |
|
|
170 | (7) |
|
11.6.1 Bulk versus single molecule experiments |
|
|
170 | (2) |
|
11.6.2 Single molecule tracking experiments |
|
|
172 | (1) |
|
11.6.3 Localization-based super-resolution microscopy |
|
|
173 | (2) |
|
11.6.3.1 Photophysics of the stochastic excitation of organic fluorophores |
|
|
175 | (2) |
|
11.6.4 A localization-based super-resolution experiment |
|
|
177 | (1) |
|
11.7 Multifocal plane microscopy |
|
|
177 | (10) |
|
11.7.1 Focal plane spacing and magnification |
|
|
179 | (1) |
|
11.7.2 Transferrin trafficking in epithelial cells |
|
|
180 | (1) |
|
11.7.3 Imaging the pathway preceding exocytosis |
|
|
181 | (6) |
|
|
187 | (18) |
|
12.1 Photoelectric effect |
|
|
187 | (1) |
|
|
188 | (1) |
|
|
188 | (5) |
|
12.3.1 Charge-coupled device (CCD) detectors |
|
|
190 | (1) |
|
12.3.2 Complementary metal-oxide-semiconductor (CMOS) detectors |
|
|
191 | (1) |
|
12.3.3 Electron-multiplying charge-coupled device (EMCCD) detectors |
|
|
192 | (1) |
|
12.4 Randomness of photon detection and detector noise sources |
|
|
193 | (1) |
|
12.5 Grayscale and color cameras |
|
|
194 | (2) |
|
12.6 Specifications of image detectors |
|
|
196 | (3) |
|
12.7 Measurements of detector specifications |
|
|
199 | (6) |
|
12.7.1 Determination of CCD and CMOS detector specifications |
|
|
199 | (1) |
|
|
199 | (1) |
|
12.7.1.2 Linearity of the response |
|
|
200 | (1) |
|
12.7.1.3 Estimation of electron-count-to-DU conversion factor |
|
|
201 | (1) |
|
12.7.1.4 Estimation of readout noise mean and variance |
|
|
202 | (1) |
|
12.7.1.5 Estimation of mean of dark current |
|
|
202 | (1) |
|
12.7.2 Determination of EMCCD detector specifications |
|
|
202 | (1) |
|
|
202 | (1) |
|
12.7.2.2 Estimation of electron-count-to-DU conversion factor |
|
|
203 | (1) |
|
12.7.2.3 Estimation of readout noise mean and variance |
|
|
204 | (1) |
|
|
205 | (18) |
|
13.1 Reflection and refraction |
|
|
205 | (4) |
|
|
205 | (1) |
|
|
205 | (1) |
|
|
206 | (1) |
|
13.1.4 Total internal reflection |
|
|
207 | (1) |
|
13.1.5 Extreme rays in microscopy optics |
|
|
207 | (2) |
|
|
209 | (4) |
|
13.2.1 Focal points and focal planes |
|
|
210 | (1) |
|
|
211 | (1) |
|
13.2.3 Lensmaker's formula and lens formula |
|
|
211 | (2) |
|
|
213 | (5) |
|
13.3.1 Lateral magnification |
|
|
213 | (3) |
|
13.3.2 Axial magnification |
|
|
216 | (2) |
|
13.3.3 Dependence of lateral magnification on axial position |
|
|
218 | (1) |
|
13.4 Applications to microscopy |
|
|
218 | (5) |
|
|
223 | (40) |
|
14.1 Wave description of light |
|
|
223 | (6) |
|
|
223 | (1) |
|
14.1.1.1 Planes of identical phase |
|
|
224 | (1) |
|
14.1.1.2 Speed of wave propagation |
|
|
225 | (1) |
|
14.1.1.3 Wave number and wavelength |
|
|
226 | (1) |
|
14.1.1.4 Propagation in different media |
|
|
226 | (1) |
|
14.1.1.5 Optical path length |
|
|
227 | (1) |
|
|
227 | (1) |
|
14.1.2.1 Converging and diverging spherical waves |
|
|
228 | (1) |
|
14.1.3 Spatial part of a wave |
|
|
228 | (1) |
|
14.2 What does a camera detect? |
|
|
229 | (1) |
|
14.3 Effect of a thin lens on waves |
|
|
230 | (4) |
|
14.4 Huygens-Fresnel principle and Fresnel integral |
|
|
234 | (3) |
|
14.4.1 Huygens-Fresnel principle |
|
|
235 | (2) |
|
14.5 Imaging through a thin lens |
|
|
237 | (14) |
|
14.5.1 Amplitude point spread function |
|
|
239 | (1) |
|
14.5.2 Convolution description |
|
|
240 | (1) |
|
14.5.3 Relationship to geometrical optics |
|
|
241 | (1) |
|
14.5.4 Point spread function and Fourier transformation |
|
|
241 | (2) |
|
14.5.4.1 In-focus point spread function |
|
|
243 | (1) |
|
14.5.5 Imaging with defocus and the 3D point spread function |
|
|
244 | (3) |
|
14.5.5.1 3D point spread function evaluated on the optical axis |
|
|
247 | (2) |
|
14.5.5.2 Depth of field and depth of focus |
|
|
249 | (2) |
|
14.5.5.3 Heuristic 3D resolution criterion |
|
|
251 | (1) |
|
14.6 Convolution for intensity profiles |
|
|
251 | (4) |
|
|
255 | (4) |
|
|
259 | (4) |
|
|
263 | (2) |
|
|
265 | (2) |
|
15 From Photons to Image: Data Models |
|
|
267 | (1) |
|
15.1 Accounting for each photon: fundamental data model |
|
|
267 | (1) |
|
15.1.1 Temporal component of photon detection -- Poisson process |
|
|
268 | (2) |
|
15.1.1.1 Mean number of detected photons |
|
|
270 | (2) |
|
15.1.2 Spatial component of photon detection -- spatial density function |
|
|
272 | (1) |
|
15.1.2.1 Translational invariance and image function |
|
|
273 | (3) |
|
15.1.3 Background component |
|
|
276 | (1) |
|
|
277 | (1) |
|
15.2 Practical data models |
|
|
278 | (15) |
|
15.2.1 Poisson data model |
|
|
279 | (5) |
|
15.2.2 CCD/CMOS data model |
|
|
284 | (1) |
|
15.2.3 Deterministic data model |
|
|
285 | (1) |
|
15.2.3.1 Gaussian approximation for the CCD/CMOS data model |
|
|
286 | (1) |
|
|
286 | (2) |
|
15.2.4.1 High gain approximation for the EMCCD data model |
|
|
288 | (1) |
|
15.2.4.2 Gaussian approximation for the EMCCD data model |
|
|
289 | (4) |
|
|
293 | (20) |
|
16.1 Maximum likelihood estimation |
|
|
293 | (4) |
|
16.1.1 Example 1: mean of a Poisson random variable |
|
|
294 | (1) |
|
16.1.2 Example 2: mean of a Gaussian random variable |
|
|
295 | (2) |
|
16.2 Log-likelihood functions for the image data models |
|
|
297 | (5) |
|
16.2.1 Log-likelihood function for the fundamental data model |
|
|
297 | (2) |
|
16.2.1.1 Example 3: Localization of an object with a 2D Gaussian image profile |
|
|
299 | (1) |
|
16.2.2 Log-likelihood functions for the practical data models |
|
|
300 | (2) |
|
16.3 Obtaining the maximum likelihood estimate |
|
|
302 | (1) |
|
16.4 Maximum likelihood estimation and least squares estimation |
|
|
303 | (1) |
|
|
304 | (4) |
|
16.5.1 Example 1: sample mean |
|
|
304 | (1) |
|
16.5.2 Example 2: sample variance |
|
|
304 | (2) |
|
16.5.3 Example 3: center of mass as an object location estimator under the fundamental data model |
|
|
306 | (2) |
|
16.6 Variance of an estimator |
|
|
308 | (5) |
|
16.6.1 Example 1: mean of a Poisson and a Gaussian random variable |
|
|
308 | (1) |
|
16.6.2 Example 2: center of mass as an object location estimator under the fundamental data model |
|
|
309 | (2) |
|
16.6.3 Example 3: center of mass as an object location estimator under a fixed photon count data model |
|
|
311 | (2) |
|
17 Fisher Information and Cramer-Rao Lower Bound |
|
|
313 | (18) |
|
17.1 Cramer-Rao inequality |
|
|
313 | (5) |
|
17.1.1 Sketch of derivation of Cramer-Rao lower bound |
|
|
314 | (2) |
|
17.1.2 Multivariate Cramer-Rao lower bound |
|
|
316 | (1) |
|
17.1.3 Example 1: mean of a Poisson random variable |
|
|
317 | (1) |
|
17.1.4 Example 2: mean of a Gaussian random variable |
|
|
318 | (1) |
|
17.2 Fisher information for the fundamental data model |
|
|
318 | (4) |
|
17.2.1 Example: known photon detection rate |
|
|
320 | (1) |
|
17.2.2 Example: known photon distribution profile |
|
|
321 | (1) |
|
17.3 Fisher information for the practical data models |
|
|
322 | (5) |
|
17.3.1 Noise coefficient and the Fisher information |
|
|
323 | (4) |
|
17.4 Noise coefficient analysis of the pixel signal level |
|
|
327 | (3) |
|
17.4.1 Noise coefficient -- an in-depth look |
|
|
327 | (1) |
|
17.4.2 Noise coefficient for CCD/CMOS detectors |
|
|
327 | (1) |
|
17.4.3 EMCCD detectors as low-light detectors |
|
|
328 | (1) |
|
17.4.4 Comparison of CCD/CMOS and EMCCD detectors |
|
|
329 | (1) |
|
17.5 Fisher information for multi-image data |
|
|
330 | (1) |
|
18 Localizing Objects and Single Molecules in Two Dimensions |
|
|
331 | (40) |
|
18.1 Object localization as a parameter estimation problem |
|
|
331 | (2) |
|
18.2 Example: estimating the location of a single molecule |
|
|
333 | (2) |
|
18.3 How well can the location of an object be estimated? |
|
|
335 | (5) |
|
18.3.1 Bias of location estimation |
|
|
335 | (3) |
|
18.3.1.1 Bias of the center of mass as a location estimator under the practical data models |
|
|
338 | (1) |
|
18.3.2 Variance of location estimation |
|
|
338 | (2) |
|
18.4 Estimation of other parameters |
|
|
340 | (1) |
|
18.5 Cramer-Rao lower bound for location estimation -- fundamental data model |
|
|
340 | (8) |
|
18.5.1 Cramer-Rao lower bound for the Airy image function |
|
|
344 | (2) |
|
18.5.2 Cramer-Rao lower bound for the 2D Gaussian image function |
|
|
346 | (1) |
|
18.5.3 Extensions to further experimental situations |
|
|
347 | (1) |
|
18.6 Cramer-Rao lower bound for location estimation -- practical data model |
|
|
348 | (8) |
|
18.6.1 Poisson data model -- effects of pixelation, finite image size, and background noise |
|
|
349 | (2) |
|
18.6.2 Localizing objects from CCD/CMOS and EMCCD images |
|
|
351 | (3) |
|
18.6.3 Object location makes a difference |
|
|
354 | (2) |
|
18.7 Efficiency of estimators: how well is the behavior of estimators described by the Cramer-Rao lower bound? |
|
|
356 | (2) |
|
18.7.1 Fundamental data model |
|
|
356 | (1) |
|
18.7.2 Practical data models |
|
|
357 | (1) |
|
|
358 | (2) |
|
18.8.1 Gaussian approximations for the CCD/CMOS and EMCCD data models |
|
|
359 | (1) |
|
18.8.2 Inverse square root approximation of the dependence on the photon count |
|
|
360 | (1) |
|
18.9 Lower bound as a tool for the design of data analysis |
|
|
360 | (3) |
|
18.9.1 Choosing the region of interest |
|
|
361 | (1) |
|
18.9.2 Improving estimation performance by adding images |
|
|
362 | (1) |
|
18.10 Example: single molecule localization from experimentally acquired images |
|
|
363 | (8) |
|
18.10.1 Choice of data model based on the detector used |
|
|
365 | (1) |
|
18.10.2 Modeling the image of the molecule and the background component |
|
|
365 | (1) |
|
18.10.3 Determining the "known" parameters |
|
|
366 | (1) |
|
18.10.4 Location estimates |
|
|
367 | (1) |
|
|
367 | (1) |
|
18.10.6 Assessing the standard deviation of the localization |
|
|
368 | (3) |
|
19 Localizing Objects and Single Molecules in Three Dimensions |
|
|
371 | (24) |
|
19.1 Parameter estimation for object localization in three dimensions |
|
|
371 | (1) |
|
19.2 Cramer-Rao lower bound for 3D location estimation -- fundamental data |
|
|
372 | (6) |
|
19.2.1 3D localization of a point source |
|
|
374 | (4) |
|
19.3 Cramer-Rao lower bound for 3D location estimation -- practical data |
|
|
378 | (1) |
|
19.4 Depth discrimination problem |
|
|
379 | (2) |
|
19.5 Dependence of lateral location estimation on the axial position |
|
|
381 | (1) |
|
19.6 Multifocal plane microscopy |
|
|
382 | (13) |
|
19.6.1 Estimating the axial location from MUM data |
|
|
384 | (2) |
|
19.6.2 Experimental example |
|
|
386 | (1) |
|
19.6.3 Maximum likelihood localization with simulated data |
|
|
386 | (3) |
|
19.6.4 Overcoming the depth discrimination problem |
|
|
389 | (2) |
|
19.6.5 Zero Fisher information and the depth discrimination problem |
|
|
391 | (1) |
|
19.6.6 Experimental design: finding appropriate focal plane spacings |
|
|
392 | (1) |
|
19.6.7 Further approaches to address the depth discrimination problem |
|
|
393 | (2) |
|
|
395 | (16) |
|
20.1 Resolution as a parameter estimation problem |
|
|
395 | (1) |
|
20.2 Cramer-Rao lower bound for distance estimation -- fundamental data |
|
|
395 | (2) |
|
20.3 Two in-focus objects: an information-theoretic Rayleigh's criterion |
|
|
397 | (3) |
|
20.4 Two objects in 3D space |
|
|
400 | (5) |
|
20.5 Cramer-Rao lower bound for distance estimation -- practical data |
|
|
405 | (6) |
|
|
411 | (16) |
|
21.1 The deconvolution problem |
|
|
411 | (2) |
|
|
413 | (1) |
|
21.2.1 Linear algebra formulation |
|
|
414 | (1) |
|
21.3 Linear least squares algorithm |
|
|
414 | (5) |
|
21.3.1 Condition number of a matrix |
|
|
415 | (1) |
|
21.3.1.1 Example of an ill-conditioned least squares problem |
|
|
416 | (1) |
|
21.3.2 Regularization of the least squares problem |
|
|
416 | (1) |
|
21.3.2.1 Example continued: regularization of the ill-conditioned least squares problem |
|
|
417 | (1) |
|
21.3.3 A Fourier transform approach |
|
|
418 | (1) |
|
21.4 Maximum likelihood formulation |
|
|
419 | (2) |
|
21.4.1 Expectation maximization algorithm |
|
|
419 | (2) |
|
21.5 Positron emission tomography |
|
|
421 | (6) |
|
21.5.1 Deconvolution for the Poisson data model |
|
|
424 | (1) |
|
21.5.2 An illustrative example |
|
|
425 | (2) |
|
|
427 | (1) |
|
|
427 | (1) |
|
22.1.1 Spatial Poisson processes |
|
|
428 | (1) |
|
22.2 Intensity functions of spatial processes |
|
|
429 | (1) |
|
22.2.1 Computing the intensity functions |
|
|
430 | (1) |
|
22.2.2 Stationary point processes |
|
|
431 | (1) |
|
22.3 K function and L function |
|
|
432 | (7) |
|
22.3.1 An example of an inhibition process |
|
|
433 | (2) |
|
22.3.2 Estimating the K function |
|
|
435 | (4) |
|
|
439 | (6) |
|
|
445 | |
|
Online Appendix -- Mathematical Background /www.routledge.com/9781138598980 |
|
|
1 | (1) |
|
A Probability and Statistics |
|
|
1 | (8) |
|
A.1 Tutorial: Poisson and Gaussian random variables |
|
|
1 | (4) |
|
A.1.1 Poisson random variables |
|
|
3 | (1) |
|
A.1.1.1 Additivity of Poisson random variables |
|
|
4 | (1) |
|
A.1.2 Gaussian random variables |
|
|
4 | (1) |
|
A.2 Expectation of a Poisson random variable given a sum of Poisson random variables |
|
|
5 | (2) |
|
A.3 Additivity of Fisher information matrices |
|
|
7 | (2) |
|
|
9 | (2) |
|
|
9 | (1) |
|
B.2 Taylor series approximation |
|
|
9 | (1) |
|
B.3 Change of variables theorem |
|
|
9 | (2) |
|
B.3.1 Change of Cartesian coordinates to polar coordinates |
|
|
10 | (1) |
|
|
11 | (6) |
|
|
11 | (1) |
|
C.1.1 Fourier transform of circularly symmetric functions |
|
|
12 | (1) |
|
C.2 Discrete Fourier transform |
|
|
12 | (2) |
|
C.3 Multidimensional discrete Fourier transform |
|
|
14 | (3) |
|
D Least Squares Minimization |
|
|
17 | (4) |
|
D.1 Least squares minimization problem |
|
|
17 | (2) |
|
D.2 Linear least squares in the Fourier domain |
|
|
19 | (2) |
|
E Fisher Information for the Fundamental Data Model |
|
|
21 | (8) |
|
F Fisher Information for the Deterministic Data Models |
|
|
29 | (2) |
|
F.1 Simple form of the deterministic data model |
|
|
29 | (1) |
|
F.2 Gaussian approximation for the CCD/CMOS data model |
|
|
30 | (1) |
|
F.3 Gaussian approximation for the EMCCD data model |
|
|
30 | (1) |
|
G Models of EMCCD Electron Multiplication |
|
|
31 | (12) |
|
G.1 Geometric multiplication-based EMCCD probability mass function |
|
|
31 | (6) |
|
G.1.1 Branching processes |
|
|
31 | (1) |
|
G.1.2 Electron multiplication as a branching process |
|
|
32 | (1) |
|
G.1.3 Geometric distribution of offspring electrons |
|
|
32 | (1) |
|
G.1.4 Probability generating function of output electron count given one initial electron |
|
|
32 | (1) |
|
G.1.5 Probability generating function of output electron count given initial electrons |
|
|
33 | (1) |
|
G.1.6 Probability mass function of output electron count given initial electrons |
|
|
33 | (3) |
|
G.1.7 Probability mass function of output electron count |
|
|
36 | (1) |
|
G.2 Exponential multiplication-based EMCCD probability density function |
|
|
37 | (1) |
|
G.3 Geometric multiplication-based EMCCD noise coefficient |
|
|
38 | (2) |
|
G.4 Exponential multiplication-based EMCCD noise coefficient |
|
|
40 | (3) |
Notes |
|
43 | (2) |
Exercises |
|
45 | (406) |
Figure Credits |
|
451 | (6) |
Bibliography |
|
457 | (8) |
List of Symbols |
|
465 | (4) |
Index of Names |
|
469 | (2) |
Index |
|
471 | |