image resolution

Question 1

no universal definition
resolution is NOT simply given by …….(i.e. sampling rate)

general definition:
smallest detail that can be distinguished

Answer 1

resolution is not simply given by pixel size (i.e. sampling rate

Question 2

factors affecting resolution

Answer 2

light quality
optics quality
detector quality
algorithm quality
noise

Question 3

resouliton criteria depends on …..

Answer 3

resouliton criteria depends on context

detector characterization
microscopy

Question 4

detector characterization

Answer 4

Full Width of Half Maximum (FWHM) of Point Spread Function (PSF)

10% Modulation Transfer Function (MTF)

Question 5

microscopy

Answer 5

numerical aperture (NA)

Question 6

LTI systems can be fully characterized by

Answer 6

LTI systems can be fully characterized by h(x)
impulse response

Question 7

Point Spread Function (PSF)

Answer 7

PSF is the impulse response of an imaging system (response to a point source)

Question 8

PSF describes …….

Answer 8

PSF describes the blurring (spreading) of an optical system

𝑖𝑚𝑎𝑔𝑒 = 𝑜𝑏𝑗𝑒𝑐𝑡 ⨂ 𝑃𝑆𝐹

PSF = h(x)

Question 9

if ,PSF depends on location, then its not

Answer 9

Not LTI

Question 10

FWHM is often estimated by

Answer 10

fitting a (2D) Gaussian to the PSF

Question 11

Numerical aperture (NA) Commonly used in

Answer 11

Commonly used in microscopy

Question 12

NA gives the range of

Answer 12

NA gives the range of angles which the system can accept or emit light

Question 13

𝑛𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙 𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒 𝑁𝐴 =

Answer 13

𝑛 ∙ sin 𝜃
𝑛 = 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑑𝑖𝑢𝑚

sin 𝜃 = 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒

Question 14

How to measure PSF?

Answer 14

not directly measurable, due to noise
indirect methods needed

Question 15

Transfer function types

Answer 15

Optical transfer function (OTF)
Modulation transfer function (MTF)

Question 16

Optical Transfer Function describes

Answer 16

how a system affects an oscillating signal
with well-defined frequency

Question 17

OTF is Fourier transform of

Answer 17

PSF

Question 18

Amplitude of OTF is known as

Answer 18

modulation transfer function (MTF)

Question 19

Phase of OTF is known as

Answer 19

phase transfer function (PTF)

Question 20

OTF can be written as

Answer 20

𝑂𝑇𝐹 = 𝑀𝑇𝐹 ∙ exp(−𝑖 (𝑃𝑇𝐹)) = 𝐹𝑇{𝑃𝑆𝐹}

Question 21

Modulation transfer function (MTF) describes

Answer 21

how an oscillating signal changes in amplitude due to system

Question 22

Resolution sometimes defined as

Answer 22

spatial frequency at 10% of MTF or FWHM PSF

Question 23

OTF of system is the product of the OTFs of the individual subsystems (linear)

Answer 23

𝑜𝑢𝑡𝑝𝑢𝑡 𝑢 = 𝑖𝑛𝑝𝑢𝑡( 𝑢) ∙ 𝑂𝑇𝐹 (𝑜𝑝𝑡𝑖𝑐𝑠) ∙ 𝑂𝑇𝐹 (𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟) ∙𝑂𝑇𝐹 (𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 )∙ 𝑂𝑇𝐹 (𝑎𝑙𝑔𝑜𝑟𝑖𝑡ℎ𝑚𝑠 )∙ …

Question 24

naive’ deconvolution

Answer 24

𝑓’ = 𝐹𝑇^−1( G/H)

Question 25

in deconvolution, noise term dominates
for

Answer 25

high frequencies

Question 26

Problems of “naive” deconvolution

Answer 26

• numerically unstable (division by zero)
• no accounting for Signal to Noise Ratio, SNR
  (increase of noise at high frequencies)

Question 27

more sophisticated methods instead of naive deconv

Answer 27

Wiener deconvolution (Least squares optimization, with known MTF and NPS)

Richardson-Lucy deconvolution iterative, known PSF)

Blind deconvolution (unknown PSF)

Question 28

Wiener deconvolution minimizes

Answer 28

least squares error

Question 29

Wiener filter W =

Answer 29

𝑊 =(1/𝐻)*{(|H|^2)/(H|^2) + (NPS/SPS))}
NPS: 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 :|𝑁(𝑢, 𝑣)|^2
SPS: Signal Power Spectrum (SPS),

Question 30

In practice one often neglects the ………….. dependence of NPS(u,v) and SPS(u,v) , which usually is not known and takes NPS/SPS as a ………..

Answer 30

In practice one often neglects the frequency dependence of NPS(u,v) and SPS(u,v) which usually is not known and takes NPS/SPS as a single number.

Question 31

𝑊𝑖𝑒𝑛𝑒𝑟“ 𝑑𝑒𝑐𝑜𝑛𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑤𝑜𝑟𝑘𝑠 𝑏𝑒𝑡𝑡𝑒𝑟,
𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑡ℎ𝑒 𝑖𝑚𝑝𝑎𝑐𝑡 of

Answer 31

𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 𝑖𝑠 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑 𝑓𝑜𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠 𝑤𝑖𝑡ℎ 𝑝𝑜𝑜𝑟 𝑆𝑁𝑅

Question 32

How can we directly measure the Point-Spread-Function?

Answer 32

We cannot measure the PSF directly.