Optics

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Optics Image Formation

• October 6, 2008
• Overview of Microscopy
• Dr. Behonick

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Topics for today

• Components of light microscopes
• Illumination
• Köehler Illumination
• Optics
• Numerical aperture
• Diffraction
• Resolution
• Optical path length
• DIC
• Image Formation
• Dynamic range
• Histograms
• Saturation

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Components of light microscopes
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What all the writing on the objective means
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What all the writing on the objective means

• optical tubelength of microscope (in mm)
• tubelength of microscope for which objective is
  intended
• tubelength distance from nosepiece opening
  where objective mounted to top edge of
  observation tubes (where ocular eyepieces mounted)

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What all the writing on the objective means

• coverglass thickness for which objective is
  corrected (in mm)
• designation - objective performance
  independent of coverglass thickness
• planochromat objective
• normal achromatic correction
• also corrected to eliminate/reduce field
  curvature
• field curvature optical aberration due to focal
  plane being spherical rather than planar
  apparent bending of field of view

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What all the writing on the objective means

• N.A. (numerical aperture)
• dimensionless number that characterizes range of
  angles over which system can accept or emit light
• takes into account refractive index of medium in
  which lens is working (e.g. - air vs. oil)
  maximum cone of light that can enter/exit lens
• indicates resolving power of lens
• larger N.A. collects more light, brigter image
  better resolution of fine details
• ratio of objective's magnification to N.A can
  predict performance of objective

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What all the writing on the objective means
water immersion objective
objective magnification
objective N.A.
coverglass thickness (mm) for which objective
is corrected
optical tubelength of microscope (mm)
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Review Components to Know
oculars
iris diaphragm
nosepiece/ turret
objectives
coarse focus
fine focus
stage
condenser
stage controls
light source
field diaphragm
rheostat
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Illumination
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Köehler Illumination

• why?
• proper alignment of illumination source for
  transmitted light microscopy
• aligning condenser lens to ensure
• optimal resolution
• even lighting of image (consistently lit
  throughout)
• no contrast artifacts

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Köehler Illumination

• Moderately close field diaphragm (displayed
  unsharp)
• Focus diaphragm image by slightly raising or
  lowering the condenser
• Center diaphragm image in field of view using
  condenser positioning screws
• Open field diaphragm so it just disappears from
  field of view
• Adjust contrast using aperature diaphragm. If
  specimen is of moderate contrast, about 2/3 of
  rear lens element of objective should be
  illuminated

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Optics
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Numerical aperture
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Numerical Aperture (NA)

• tells you how much of light cone objective can
  gather
• important consideration in resolution

cone of light
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NA

• NA n (sin f)
• n refractive index of medium between coverslip
  front lens of objective
• f 1/2 angle of cone of light
• (i.e. 1/2 angular aperture)

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Optimal NA
NA n (sin f)

• AIR
• n 1.0
• ? NA of 1 is theoretical max for dry lenses (.95
  is real max)
• OIL
• n 1.5
• ? NA of 1.5 is theoretical max for oil immersion
  lenses (1.46 is real max)

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NA and magnification
NA n (sin f)

• as magnification increases, f increases so NA
  increases (while focal length decreases)

Note the 1/2 angle can be referred to as f, a, m
etc.
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NA and magnification
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NA and magnification
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NA and LOW magnification
light rays
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NA and MID magnification
light rays
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NA and HIGH magnification
light rays
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Tradeoffs

• high magnification, oil objective
• best NA, so best spatial resolution
• most brightness
• tradeoffs less contrast, less field of view,
  less depth of field

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NA

• magnification NA both important for resolution
• objective w/ high NA can have more resolving
  power than one with more magnification but
  smaller NA
• example
• 63x 1.4 NA objective resolution .24 mm
• 100x 1.3 NA objective resolution .26 mm
• Murphy, page 54 Table 4

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NA Köehlering

• closing iris (condenser) diaphragm decreases NA
  of condenser
• tradeoff contrast vs. resolution
• open condensor diapraghm
• more effective NA
• more resolution
• less contrast
• less depth of focus
• closing it down has opposite effects
• general starting point 2/3 open

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NA

• rule of thumb
• magnification should be 500-1000x NA
• more than that is empty magnification

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Diffraction
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Abbes theory of image formation

• The microscope image is the interference effect
  of a diffraction phenomenon

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Diffraction of waves
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Diffraction

• diffraction pattern through 2 slits gives striped
  image
• why?
• constructive destructive interference between
  waves

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Diffraction
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Diffraction of light

• light from point source passing through aperture
  diffracts
• aperture can be eye or objective
• pattern of diffraction Airy disk (or point
  spread function, PSF)

images from http//micro.magnet.fsu.edu/primer/ind
ex.html
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Airy Discs Spatial Resolution

• smaller Airy disc, better spatial resolution
• resolution ability to distinguish 2 spots as
  separate

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Airy Discs Spatial Resolution

• big airy discs so we cant resolve these 2 spots

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Airy Discs Spatial Resolution

• smaller airy discs so we can resolve the same 2
  spots

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Airy Discs Spatial Resolution

• How do we get a smaller Airy disc (for better
  resolution)?
• increase NA of objective!
• n.b. - increasing magnification also helps

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Airy Discs Spatial Resolution

• low NA
• bigger Airy
• lower resolution

• high NA
• smaller Airy
• higher resolution

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NA Airy Disc Size
smaller Airy/ better resolution
more magnification/NA
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Airy tutorial

• http//micro.magnet.fsu.edu/primer/java/imageforma
  tion/rayleighdisks/index.html

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Resolution
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Rayleigh Criterion

• 2 spots resolvable when they meet Rayleigh
  criterion
• Airy disk of 1 spot overlaps w/ 1st order
  diffraction ring of other spot
• theyll be separated by distance (d) equal to
  radius of Airy disk
• Murphy, page 87
• http//micro.magnet.fsu.edu/primer/java/imageforma
  tion/rayleighdisks/

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Rayleigh Limit
OK
Too close
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Resolving Power

• can use Rayleigh limit to define best possible
  resolving power for an objective
• d 0.61 ?/NAobj
• d minimum resolved distance in mm
• when condenser NA gt objective NA
• n.b. - 0.61 has to do with the geometry of
  circles!

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Resolving Power

• d 1.22 ?/Nacond NAobj
• d minimum resolved distance in mm
• when condenser NA lt objective NA

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Optical path length
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Optical Path

Imagine tracing the wave as it goes up and down
how far overall did you go?
end here
start here
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Optical Path

• OPL (optical path length) nd
• n refractive index
• d distance traveled
• n.b. - distance traveled (d) determined by
  thickness of specimen
• ? thickness of specimen material it is made of
  (n) both contribute to OPL of transmitted light
• Murphy, pages 68-69

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Optical Path
Two specimens of same thickness, different
n. Which has the longer OPL?
bigger n
A
B
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Optical Path

• bigger n ? longer OPL
• thicker specimen ? longer OPL
• OPL also wavelength dependant

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Optical Path

• Consider optical path of light wavefronts through
  slide w/ specimen in aqueous solution

direction of light
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Optical Path

• Consider optical path of light wavefronts through
  slide w/ specimen in aqueous solution

different optical path lengths!
direction of light
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Optical Path

• Differences in optical path (D) can readout as
  contrast

t
D (n1-n2) t
n1
n2
direction of light
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Optical Path

• differences in optical path (OPD) are used by
  contrast-generating techniques such as DIC
  phase
• Interactive
• http//www.microscopyu.com/tutorials/java/phaseco
  ntrast/phasespecimens/index.html
• http//www.microscopyu.com/tutorials/java/phaseco
  ntrast/opticalpathlength/index.html

n1
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DIC
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Differential Interference Contrast

• a.k.a. - Nomarski
• turns gradients in optical path into gradients in
  intensity, generating contrast
• Murphy, pages 153-156

n1
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DIC

• looks 3D, but be careful when interpreting the
  images!
• when you see contrast, you are seeing some
  combination of differences in n /or differences
  in thickness
• ? best for regions w/ gradients in n thickness
• e.g. - edge of cell or organelle.
• n.b. - cant use plastic dishes

n1
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DIC
http//www.microscopyu.com/
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5) a polar selects components so interference
can occur
4) recombines light
3) phase shifts/optical path differences occur
2) splits the light
1) polarizes light
image from http//micro.magnet.fsu.edu/primer/inde
x.html
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DIC
http//www.microscopyu.com/
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Image formation
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• focal plane flat plane perpendicular to optical
  axis onto which lens focuses image
• optical axis path along which light propagates
  through system

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• focal length distance from center of lens to
  focal point how strongly optical system
  focuses/diffuses light
• shorter focal length ? greater optical power
• convex lens positive focal length
• concave lens negative focal length

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Dynamic Range
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Dynamic Range

• Dynamic range (DR) difference between dimmest
  brightest value of steps in between
• i.e. - of grey levels
• grey levels due to intensity of signal
• more signal ? lighter
• less signal ? darker
• Murphy, page 274

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Bit Depth in CCD Cameras

• CCD charge coupled device (way image signal is
  read out from chip)
• of grey levels (different intensities) depends
  on bit depth
• bit depth bits used to represent color of a
  single pixel in image
• 4 bits 16 levels
• 8 bits 256 levels
• 10 bits 1024 levels
• 12 bits 4,096
• 16 bits 65,536
• 0 black max value white

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Bit Depth

• bit depth property of ADC (analog to digital
  converter, a.k.a the digitizer) of CCD camera
• microscopy CCD cameras tend to be 8, 10, or 12
  bit cameras

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Dynamic Range Bit Depth

• consider DR bit depth camera can deliver
• n.b. - computer monitor or printer may be only 8
  bits
• even if display has few grey levels, take
  original image w/ many grey levels (for
  quantification, mathmatical processing by
  software, etc.)
• Murphy, page 275

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Histograms
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Histogram

• representation of dynamic range of your system
  where particular image falls w/in that dynamic
  range
• want to optimize image to use full dynamic range
  w/o saturating any pixels

of pixels
0 black
top value white
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Examples

• not optimal (not using full DR)

of pixels

• much better (uses most of DR)

of pixels
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Saturation
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Saturation

• can occur _at_ either end of dynamic range
• in saturated pixels you can no longer distinguish
  between different grey levels
• ? you are losing data!
• use histogram to figure this out
• if there are a lot of black or white pixels, you
  have probably saturated that end of dynamic range

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Saturation Rules

• optimally, you should avoid saturation _at_ either
  end of DR
• you can decide to let dark pixels be slightly
  saturated if you think there is no info in them,
  but make a note of it in your image log. usually
  dark pixels are background in a fluorescence
  image
• you rarely want to saturate bright pixels in a
  fluorescence image since that is your data

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Saturation

• not saturated

• saturated (at both ends)

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Saturation

• saturated (at both ends)

these pixels are lumped in together as white
these pixels are lumped in together as black

• what is really happening

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Saturation

• saturated (at both ends)

info is lost

• why you dont want to saturate

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References

• Giorgi, G. Lecture 9. Merritt College Biology
  035, 27 March 2008.
• Giorgi, G. Lecture 10. Merritt College Biology
  035, 1 April 2008.
• Objective Markings What they mean.
  Micrographia. 1 Oct 2008. lthttp//www.micrographia
  .com/tutoria/micbasic/micbpt02/micb0200/objmrk01.h
  tmgt