image resolution Flashcards
no universal definition
resolution is NOT simply given by …….(i.e. sampling rate)
general definition:
smallest detail that can be distinguished
resolution is not simply given by pixel size (i.e. sampling rate
factors affecting resolution
light quality
optics quality
detector quality
algorithm quality
noise
resouliton criteria depends on …..
resouliton criteria depends on context
detector characterization
microscopy
detector characterization
Full Width of Half Maximum (FWHM) of Point Spread Function (PSF)
10% Modulation Transfer Function (MTF)
microscopy
numerical aperture (NA)
LTI systems can be fully characterized by
LTI systems can be fully characterized by h(x)
impulse response
Point Spread Function (PSF)
PSF is the impulse response of an imaging system (response to a point source)
PSF describes …….
PSF describes the blurring (spreading) of an optical system
𝑖𝑚𝑎𝑔𝑒 = 𝑜𝑏𝑗𝑒𝑐𝑡 ⨂ 𝑃𝑆𝐹
PSF = h(x)
if ,PSF depends on location, then its not
Not LTI
FWHM is often estimated by
fitting a (2D) Gaussian to the PSF
Numerical aperture (NA) Commonly used in
Commonly used in microscopy
NA gives the range of
NA gives the range of angles which the system can accept or emit light
𝑛𝑢𝑚𝑒𝑟𝑖𝑐𝑎𝑙 𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒 𝑁𝐴 =
𝑛 ∙ sin 𝜃
𝑛 = 𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑒𝑑𝑖𝑢𝑚
sin 𝜃 = 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑛𝑐𝑒 𝑎𝑛𝑔𝑙𝑒
How to measure PSF?
not directly measurable, due to noise
indirect methods needed
Transfer function types
Optical transfer function (OTF)
Modulation transfer function (MTF)
Optical Transfer Function describes
how a system affects an oscillating signal
with well-defined frequency
OTF is Fourier transform of
PSF
Amplitude of OTF is known as
modulation transfer function (MTF)
Phase of OTF is known as
phase transfer function (PTF)
OTF can be written as
𝑂𝑇𝐹 = 𝑀𝑇𝐹 ∙ exp(−𝑖 (𝑃𝑇𝐹)) = 𝐹𝑇{𝑃𝑆𝐹}
Modulation transfer function (MTF) describes
how an oscillating signal changes in amplitude due to system
Resolution sometimes defined as
spatial frequency at 10% of MTF or FWHM PSF
OTF of system is the product of the OTFs of the individual subsystems (linear)
𝑜𝑢𝑡𝑝𝑢𝑡 𝑢 = 𝑖𝑛𝑝𝑢𝑡( 𝑢) ∙ 𝑂𝑇𝐹 (𝑜𝑝𝑡𝑖𝑐𝑠) ∙ 𝑂𝑇𝐹 (𝑑𝑒𝑡𝑒𝑐𝑡𝑜𝑟) ∙𝑂𝑇𝐹 (𝑎𝑡𝑚𝑜𝑠𝑝ℎ𝑒𝑟𝑒 )∙ 𝑂𝑇𝐹 (𝑎𝑙𝑔𝑜𝑟𝑖𝑡ℎ𝑚𝑠 )∙ …
naive’ deconvolution
𝑓’ = 𝐹𝑇^−1( G/H)
in deconvolution, noise term dominates
for
high frequencies
Problems of “naive” deconvolution
- numerically unstable (division by zero)
- no accounting for Signal to Noise Ratio, SNR
(increase of noise at high frequencies)
more sophisticated methods instead of naive deconv
Wiener deconvolution (Least squares optimization, with known MTF and NPS)
Richardson-Lucy deconvolution iterative, known PSF)
Blind deconvolution (unknown PSF)
Wiener deconvolution minimizes
least squares error
Wiener filter W =
𝑊 =(1/𝐻)*{(|H|^2)/(H|^2) + (NPS/SPS))}
NPS: 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 :|𝑁(𝑢, 𝑣)|^2
SPS: Signal Power Spectrum (SPS),
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 ………..
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.
𝑊𝑖𝑒𝑛𝑒𝑟“ 𝑑𝑒𝑐𝑜𝑛𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑤𝑜𝑟𝑘𝑠 𝑏𝑒𝑡𝑡𝑒𝑟,
𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝑡ℎ𝑒 𝑖𝑚𝑝𝑎𝑐𝑡 of
𝑜𝑓 𝑛𝑜𝑖𝑠𝑒 𝑖𝑠 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒𝑑 𝑓𝑜𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠 𝑤𝑖𝑡ℎ 𝑝𝑜𝑜𝑟 𝑆𝑁𝑅
How can we directly measure the Point-Spread-Function?
We cannot measure the PSF directly.
