Basic Imaging Principles
University of Cyprus
Biomedical Imaging and Applied Optics
Basic Imaging Principles
Imaging
Real world
Opics
Sensor
2
Vision
• Sensation ≠ Perception
• Perception
•
•
•
Our understanding (conscious
interpretation) of the physical world
An interpretation of the senses
Different from what is out there
because
• Our receptors detect limited number of
existing energy forms
• The information does not reach our
brain unaltered. Some features are
accentuated and some are
suppressed
• The brain interprets the information
and often distorts it (“completes the
picture” or “feels in the gaps”) to
extract conclusions.
l i
• Interpretation is affected by cultural,
social and personal experiences
stored in our memory
3
Vision
• Eye - Sensory organ for vision
Suspensory ligament
Extrinsic eye
muscle
Choroid
Ciliary body
Lacrimal Glands
(under eyelid)
Retina
Conjunctiva
Sclera
Iris
Fovea
Pupil
Lens
Canal for tear
drainage
Pupil
Cornea
Sclera
Optic nerve
Iris
Aqueous humor
Optic disc
Vitreous humor
Circular (constrictor)
muscle runs circularly
Pupillary constriction
Circular
muscle
of iris
Radial
muscle
of iris
Pupil
Iris
Blood vessels
Radial (dilator) muscle runs
radially
Pupillary dilation
4
Vision
• Convex structures of eye
produce convergence of
diverging light rays that reach
eye
• Two structures most
important in eye’s refractive
ability are
• Cornea
• Contributes most extensively
to eye’s total refractive ability
• Refractive ability remains
constant because curvature
never changes
Sympathetic
stimulation
Relaxed
ciliary
muscle
Iris
Taut
suspensory
ligaments
• Lens
• Refractive ability can be
adjusted
dj t d b
by changing
h
i
curvature as needed for near
or far vision
(accommodation)
Flattened
weak
lens
Cornea
Sympathetic
stimulation
Contracted
ciliary
muscle
Rounded
strong
l
lens
Slackened
suspensory
ligaments
5
Vision
Far source
Near source
Normal eye (Emmetropia)
Far source focused on retina without
accommodation
Near source focused on retina with
accommodation
No accommodations
Accommodations
Nearsightedness (Myopia)–
Eyeball too long or lens too strong
1.
1
Image
out of
focus
1 Uncorrected
1.
U
t d
Focus
Far source focused in front of
retina (where retina would be in
eye of normal length)
No accommodations
No accommodations
Farsightedness (Hyperopia)–
Eyeball too short or lens too weak
Image
out of
focus
1.
Near source focused on retina
with accommodations
1. Uncorrected
Far source focused on retina
with accommodations
Focus
Accommodations
Accommodations
Near source focused behind
retina even with accommodations
6
Vision
• Retina
• Several layers of cells
• Receptor containing portion is
actually an extension of the CNS
• Macula
•
Center of vision
• Fovea
F
Direction of light
Optic nerve
• Pinhead-sized depression in
exact center of retina
P i t off mostt distinct
di ti t vision
i i
• Point
• Has only cones
Retina
Pigment layer
Choroid layer
Direction of retinal visual processing
Sclera
Front
off
retina
Back
off
retina
Fibers of
the optic
nerve
Ganglion
cell
Amacrine
cell
Bipolar Horizontal
cell
cell
Retina
Cone
Rod
Photoreceptor
cells
7
Vision
Back of retina
• Photoreceptors
Cells of
pigment layer
• Rod and cone cells
• Photopigments on the disk membranes
• Rod Æ one type
•
one pigment, high sensitivity
Cone
Outer
segment
• Cones Æ three different types
•
Red, green, blue sensing pigments, lower sensitivity
• Undergo chemical alterations when activated by
light
g
• Change the receptor potential
• Induce action potentials
• Unlike other receptors, photoreceptors hyperpolarize!
Rods
Cones
100 million per retina
3 million per retina
Vision in shades of gray
Color vision
High sensitivity to light
Low sensitivity to light
Much convergence in retinal pathways
Little convergence in retinal pathways
Night vision (from sensitivity and
convergence)
Day vision (lack sensitivity and
convergence)
Low acuity
High acuity
More numerous in periphery
Concentrated in fovea
Inner
segment
Synaptic
terminal
Rod
Discs
Mitochondria
Outer
segment
Nuclei
Inner
segment
Dendrites
of bipolar
cells
ll
Synaptic
terminal
Front
of retina
Direction
of
light
8
Vision
Blue cone
• Color Vision
Green cone
Red cone
• Perception of color
• Depends on the ratio of
stimulation of three different
cones
• Different absorption of cone
pigments
• Coded and transmitter by different
pathways
• Processed in color vision center
of primary visual cortex
• Color blindness
• Defective cone
• Colors become combinations of
two cones
• Most common = red-green color
blindness
Color
perceived
Wavelength of light (nm)
Visible
spectrum
9
Vision
10
Vision
• >30% of cortex participates in
visual information processing
• “What” and “where” pathways
• Depth Perception
• Visual field of two eyes
y slightly
g y
different
• Depth perception with one eye
• Other cues (such as size,
location, experience)
11
Vision
• Visual field
•
Area which can be seen without
moving the head) Æ overlap between
eyes
Left
Right
• Visual Pathway
y
•
•
•
•
•
•
Optic nerve
Optic chiasm
Thalamus
Optic radiation
Primary visual cortex (occipital lobe)
Higher processing areas
• Information arrives altered at the
primary visual cortex
•
Upside down and backward because
of the lens
• The left and right halves of the
brain receive information from the
left and right halves of the visual
field
Left
eye
Right
eye
1
Optic
nerve
Optic
chiasm
2
3
Optic tract
Lateral
geniculate
nucleus of
thalamus
O ti radiation
Optic
di ti
Optic lobe
12
Vision
We make cameras that act “similar” to the human eye but …
Insect Eyes
Fly
Fl
Mosquito
13
Camera Obscura
"When
When images of illuminated objects ... penetrate through a small hole into a very dark
room ... you will see [on the opposite wall] these objects in their proper form and color,
reduced in size ... in a reversed position, owing to the intersection of the rays".
Leonardo da Vinci
http://www.acmi.net.au/AIC/CAMERA_OBSCURA.html (Russell Naughton)
Slide credit: David Jacobs
14
Pinhole Cameras
• Pinhole camera
• B
Box with
ith a smallll h
hole
l iin it
• Image is upside down, but not mirrored
left-to-right
• Q
Question: Whyy does a mirror reverse
left-to-right but not top-to-bottom?
• Problems with Pinhole Cameras
• Pinhole
o e ssize
e (ape
(aperture)
tu e) must
ust be “very
ey
small” to obtain a clear image.
• However, as pinhole size is made
smaller, less light is received by image
plane.
plane
• If pinhole is comparable to wavelength
of incoming light, DIFFRACTION
effects blur the image!
• Sharpest image is obtained when:
d =2 f 'λ
• d: pinhole diameter
• Example:
p If f’ = 50mm,, λ = 600nm
(red), Æ d = 0.36mm
15
Lenses
• Image Formation using (Thin)
Lenses
Converging (focusing) Lens
• Lenses are used to avoid problems
with pinholes.
• Ideal Lens: Same p
projection
j
as
pinhole but gathers more light!
• Real Lenses
• High
g index material finite
• Two radii of curvature
• Lensmakers formula
⎛1
1 1
1 ⎞
+ = (n2 − 1)⎜⎜ − ⎟⎟
so si
⎝ R1 R2 ⎠
Diverging
g g ((defocusing)
g) Lens
(Focal length is negative)
• Focal length
⎛1
1
1 ⎞
= (n2 − 1)⎜⎜ − ⎟⎟
f
⎝ R1 R2 ⎠
16
Lenses
• Image
g formation using
g
one lens
• Ideal thin lens
D
ho
si
so 2f
f
f
hi
2f
f
f
2f
2f
f
f
2f
1 1 1
= +
f so si
• f = focal length
• si = image
i
di
distance
t
• so = object distance
• Magnification
M
ifi ti
s
h
M =− i =− i
so
ho
17
Lenses for imaging
• Imaging with two
lenses
• Depends on separation
• Interesting case -t l
telescope
f
f
f
f
4 f imaging
• equal focal lengths
• 4 f imaging
• unequal focal lengths
• magnification
ifi ti = f2/f1
f1
f1
f2
f2
Imaging telescope
18
Lenses
• Imaging scattering vs. Transparent objects
• Scattering object acts as array of sources
• Transmission object -- curvature important
• 4 f configuration
g
better
illumination
4 f imaging
2 f imaging
illumination
Scattering
f
f
f
2f
f
2f
Transmission
illum.
ill
illum.
f
f
f
f
2f
2f
19
Lenses
• Beam expanders
Galilaen
f2
• Analogous to 4 f imaging
• wavefront curvature preserved
• magnification is focal length
ratio
- f1
• independent of lens spacing
d
• Two types
• Galilaen and spatial
spatial-filter
filter
arrangements
• Galilaen easier to to set and
maintain alignment
Spatial-filter arrangement
Spatial filter for laser beam cleanup
Pinhole
aperture
Aberrated
laser beam
f
Cleaned
laser beam
f
20
Lenses
• F-number:
• (M
( is magnification)
f
)
f
f /# =
D
D
1
=
• Numerical aperture: NA = n sin φ , for small angles: NA =
2 f 2 f /#
• (n is refractive index)
2.44 f λ
1.22λ
• Focal spot diameter: d =
= 2.44λ f /# =
D
NA
2
1.22λ
⎛2f ⎞
• Depth of focus: z = 1.22λ ⎜
⎟ cos φ , for small angles: z = NA2
⎝ D ⎠
z
D
φ
d
f
21
Lenses
• Gromit captured at f/22 (left) and at f/4 (right).
22
Lenses
• Gaussian Beams
• E.g. from laser, or single mode fiber, 2w is the effective D
• Intensity profile: I = I 0 e
−2 r 2 / w 2
2
• Beam waist: w = w0 1 + ⎛⎜⎜ λz2 ⎞⎟⎟
⎝ πw0 ⎠ 2
πw0
z
=
• Confocal parameter: R
λ
• Far from waist:
w→
λz
πw0
, divergence angle: Θ =
2λ
λ
= 0.637
πw0
w0
23
Lenses
Aperture size
Standard Lens
Gaussian Beam
D
2w
Focal spot
p size
2.44 f λ
d=
D
Depth of focus
⎛2f ⎞
z = 1.22
1 22λ ⎜
⎟
D
⎝
⎠
2.54 f λ
d = 2 w0 =
2
2w
2
⎛2f ⎞
z = 1.27
1 27λ ⎜
⎟
2
w
⎝
⎠
2
24
Lenses
• Problems with Lenses
Compound (Thick) Lens
Vignetting
B
L3 L2 L1
principal planes
α
α
A
nodal points
thickness
Chromatic Abberation
more light from A than B !
Radial and Tangential Distortion
ideal
FB FG
FR
actual
ideal
actual
image
g p
plane
Lens has different refractive indices
for different wavelengths.
25
Lens Aberrations
• Lens Aberrations
•
•
•
•
•
•
•
Chromatic
Spherical
Marginal Astigmatism
Coma
Curvature of Field
Distortion
Vignetting
26
Lens Aberrations
• Chromatic Aberrations
• Longitudinal (axial)
• Various focal points on the
axis.
• Lateral (magnification)
• Different image sizes
• Result in colored ‘ghost’
images
• Material dependent
• λ dependent n
• The higher the power of the
lens, the more the chromatic
aberration.
• Correction:
• Doublet lens or triplet lens
• Change lens materials.
• Control edge thickness
27
Lens Aberrations
• Spherical Aberrations
• Spherical lens
• Peripheral rays have shorter
focal length than paraxial
rays Æ Peripheral rays
refract more than paraxial
rays.
• R
Results
lt iin out-of-focus
t ff
image.
• Wide beam aberration – not
important in narrow beam
design.
• On-axis aberration
• Correction
• Parabolic curves
• Aplanatic lens design
design.
28
Lens Aberrations
• Marginal Astigmatism
• A.k.a Oblique astigmatism
or Radial astigmatism
• Rays that propagate in two
perpendicular planes have
different foci
• Spherical lens, narrow
beam entering off-axis.
• Beam enters obliquely to
lens axis
axis, therefore effects
periphery
• Narrow beam aberration.
• Correction
• Aspheric design for high
powers and large lenses
lenses.
29
Lens Aberrations
• Coma
• Off-axis point sources
appear
pp
distorted,, like
having a tail (coma)
• Results in out-of-focus
image
• Wide beam aberration
• Correction
• parabolic curves
curves, planatic
lens design.
30
Lens Aberrations
• Curvature of Field
• A.k.a. Petzval field
curvature
• Light does not focus on a
flat focal plane. The focal
plane is curved.
• Old movie screens Æ Theyy
were curved, not flat, to
focus the sides of the movie
as well as the center.
• The retina is not a flat
plane. It is curved.
• Affects the periphery
• Correction
• minimized with corrected
curve design base curves
curves.
31
Lens Aberrations
• Distortion
• A deviation from rectilinear
projection Æ straight lines
in a scene do not remain
straight in an image
• Image is in focus, but not
shaped
h
d the
h same as the
h
object
• Usually from the presence
of apertures in the system
which distort the radial
magnification
Distortion – pincushion – high plus lens
• Correction:
• Aspheric design lenses
Distortion – barrel – high minus lens
32
Lens Aberrations
• Vignetting
g
g
• Reduction of an image's
brightness or saturation at
the periphery compared to
the image center
• Mechanical (block),
(block) optical
(front lenses block light to
the back), natural (light fall
off not by blocking
• Correction:
• Reduce aperture
• Different design
33
Fresnel Lenses
• Start with conventional lens
• Constrain optical thickness to be modulo l
• Advantage -- thinner and lighter
Fresnel vs conventional lens
34
Graded index (GRIN) lens
• Glass rod with radial index gradient
• Quadratic gradient -- high index in center
• like lens
• optical
p
p
path length
g varies q
quadratically
y from center
• Periodic focusing
• laser spot size varies sinusoidally with distance
GRIN fiber probes
GRIN rod lens
GRIN periodic focusing
35
Lenses as Fourier Transformers
• 4 f configuration
g
-- transform plane in center
Fourier transform of letter “E”
36
Image Formation
•
Image resolution
1. N
1
Number
b off pixels
i l (e.g.
(
1024 1024)
1024x1024)
2. Smallest resolvable spatial
frequency Æ smallest resolvable
p
resolution
detail = optical
•
Optical resolution
•
Rayleigh criterion
•
•
Sparrow criterion
•
•
d3dB
3 dB =
3 dB down between peaks
1.02λ
NA
d=
1.22λ
NA
Width of PSF
Aberrations degrade the resolution
D
θR
d
x
PSF
NA ≈
D
x
d
37
Image Formation
Example
• Characteristics
Ch
t i ti
•
•
Resolution: 1 mm
Field of View: 1 x 1 m
• Choice of camera
Æ 1m/1mm x 2 (Nyquist) =2000 pixels
• ≥ 4 MPixel (2000 x 2000)
• Π.χ.
χ CCD, 5 MPixel, 2x2 cm Area
•
•
•
•
si = 17 mm (c-mount)
M = 2 cm / 1 m = 2x10-2
so = s/M = 85 cm
f = 16,67
16 67 mm
• Is this optically possible?
•
•
•
•
d= Μ x 1 mm = 2 x 10-5 m
D = 2.44
2 44 λ si / d = 1.3
1 3 mm
Any lens with a diameter over 1.3 mm.
In the case of microscopic objects the
diameter may be prohibitive!
38
Image Formation
Example
• Practical Problems
•
•
f = 16,67 mm are not available
commercially
Recalculate the system
•
•
•
M = 2x10-2
f = 20 mm
Solve the equations
• Ssi = 20,4 mm
• So = 102 cm
39
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