Considerations about TVoptics for screen stations at PITZ

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Considerations about TV-optics for screen
stations at PITZ

• J.Bähr
• PITZ PPS
• DESY,March 20, 2007

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Outline

• 1.Motivation
• 2. Introduction
• 3. System with switchable lenses
• 4. Effects influencing optical imaging
• 5. Depth-of-field problem
• 6. Outlook
• 7. Summary

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1. Motivation

• A remotely controlled zoom lens is needed for a
  proper measurement of transverse emittance
• Image full screen ? beamlet
• Discuss several optical effects influencing the
  optical imaging and restriction of optical
  resolution

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2. Introduction

• Remotely controlled zoom lens at PITZ
• Experience bought system working properly but
  too small aperture gt too small signal
• Alternative several switchable lenses (similar
  to FLASH (achromats)
• Discussion of influences limiting resolution in
  optical imaging and proper methods for
  description
• Discuss depth-of focus-problem and solve the
  problem of inclined screens

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Consideration of a remotely controlled zoom lens
system at PITZ or alternatives

• History in 2006 a commercially available
  remotely controlled zoom lens was tested at PITZ
• Result in principle positive but small aperture,
  small signal

• Consequence try to develop a system ourselves
  use hand driven zoom lens and try to develop a
  motor drive no real solution, expected 3 drives
  needed and space problem) ? search for
  alternative
• Preparation of use of 12 bit digital camera

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3. System with switchable lenses3.1 concept
user demands

• Different magnifications
• Full screen
• Magnification matched to beam-let
• Intermediate case or even higher magnification

• Change the system by minimum invasion
• Keep all functions besides lens of the PITZ
  standard system

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3.2 Feature of the standard PITZ TV-system

• To avoid influence of X-rays the camera is not
  positioned straight from the screen, but at least
  one 90 degree kink is included in the optical
  axis
• Camera JAI M10 RS..???
• Application of 12 bit digital camera in
  preparation
• A ring shaped light source is used to illuminate
  the screen (if needed)

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3.2 Feature of the standard PITZ TV-system
Lead
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3.2 Feature of the standard PITZ TV-system

• A back illuminated resolution chart is used for
  calibration of the system
• Magnification
• Resolution
• This system can be included in the system by a
  switchable mirror and is situated in a plane
  corresponding to the plane of the screen

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3.3 Proposal for a system using switchable lenses

• System with 3 lenses
• Image full screen
• Magnification for minimum beam-lets
• Intermediate magnification or higher
  magnification

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3.3 Proposal for a system using switchable lenses

• Scheme

L1 L2 L3
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3.4 Imaging using a thin lens
M magnification f focal lenght a object
distance a image distance F(no) f-number F(no)
f/D D lens diameter

• Thin lens formula
• 1/f 1/a 1/a L a a
• f a a/(a a) M a/a

a f (1M) a f (11/M)
Image
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3.5 Calculation of effective aperture and
relative illumination level in image plane

• Ansatz
• I a ²/M² a Aperture angle
• Use fomulae of last slide
• Result I 1/ F(no) ² / (1M² )
• Approximation small aperture angles for larger
  angles a ? tan a
• Cases
• Mgtgt1 I 1/ F(no) ² / (M² ) (Not realized at
  PITZ)
• M 1 I 1/ 2 F(no) ²
• Mltlt 1 I 1/ F(no) ²

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3.5 Calculation of effective aperture and
relative illumination level in image plane

• Example

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3.6 Measurement of optical resolution

• For several lenses and magnifications the optical
  resolution was measured in the lab

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3.5 Measurement of optical resolution

• Compare achromat with zoom lens
• Good resolution needs high magnification
• High magnification ? small field
• Field size large axis of camera sensor back
  projected

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3.7 Considerations about choice of magnification
field size , resolution
All values calculated

• Assumed
• Sensor size 4.8 mm x 6.4 mm
• Pixel size (8.3 µm)²
• Needed Compromise Field size ? resolution

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3.7 Considerations about choice of magnification
field size , resolution

• Comment Consider the remarkable difference in
  resolution measured and calculated from pixel
  size and magnification !!
• Example
• M 1
• Resolution measured 20 Lp/mm
• Resolution calculated 60 Lp/mm
• Where comes this difference from?

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4. Effects influencing optical imaging

• Effects
• Pixel size, sensor size, magnification, pixel
  number
• Optical imaging, aberrations
• Non-ideal focus
• Diffraction
• Depth-of-focus (dof)

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4.1 Effects influencing optical imaging Pixel
size, sensor size, magnification, pixel number
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4.2 Effects influencing optical imagingOptical
imaging, aberrations

• Optical aberrations
• ideal system ? real system
• Point ? image disk, distribution with finite
  diameter (point spread function)
• Development of image disk distribution in series
  of 3rd order of aperture angle and field angle
• ? Seidel aberrations
• Besides these chromatic aberrations

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4.2 Effects influencing optical imagingOptical
imaging, aberrations

• Besides these aberrations exist higher
• order aberrations, also mixed chromatic terms
• -If aberrations negligible compared to
• diffraction ? diffraction limited

• Seidel aberrations

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4.2 Effects influencing optical imagingOptical
imaging, aberrations

• Comment
• From these list becomes clear, why a good (or
  even diffraction limited objective) consists of
  several (gt4 ) lenses
• The correction of such many aberrations needs
  many free parameters One lens has 4 2 radii,
  thickness, refractive index
• A single lens can never have high resolution
• An achromat is only corrected on chromatic
  aberration, but is not corrected on all other
  aberrations (with small restrictions) (for
  example on axis remarkable spherical aberrations).

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4.2 Effects influencing optical
imagingDiffraction

• Effect limiting resolution in some cases.
• Diffraction at the diaphragm (lens diameter)
• Causes a diffraction pattern (disk-like)
• a 0.61?/r a diffraction angle
• r D/2 lens radius ? wavelength of light
• d 2.44 ?F(no) (1M) diameter of image disk
  from diffraction ?resolution
• Example
• For M0.24, F(no) 2.4 and 500nm d 3.6 µm ?
• R(es) 275 Lp/mm low (influence on resolution)

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5. Depth-offield problem

• Image disk of diameter d
• d D ?a/a
• d ?a/F(no)/(1M)

• Example
• F(no)2.4, M0.24, f120mm
• Defocus 0.1mm
• ? Resolution 30 Lp/mm (34µm)

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5.Depth-offield problem

• Example

• F(no)1.6, M0.12, Defocus 0.1mm, f80mm
• Resolution 18 Lp/mm (55µm)
• These examples show the importance of good
  focusing!
• It is obvious that the defocusing can limit the
  resolution!
• Comparison Resolution
• Calculated 18 Lp/mm
• Measured 8 Lp/mm
• Defocused 30 Lp/mm
• Calcul. defoc. 15 Lp/mm combined

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5.Depth-offield problem5.1 Inclined screen
without optical correction

• Inclined screen 45 deg
• All off-axis points are out of focus!!

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5.Depth-offield problem5.2 Inclined screen with
optical correction

• Solve the dof problem of inclined screens
• The Scheinpflug condition

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5.The MTF formalism

• Very convenient and elegant formalism
• Contains much more information than one single
  figure Resolution, considers functions
• Point-like object ? imaging? image disk
• d-function ? imaging ? Point spread function P(x)
• MTF modulation transfer function M(?)
• P(x) ? Fourier transform (FT) ? M(?)
• In linear system
• For several effects contributing to optical
  imaging
• M1, M2, M3, M4(aberrations, diffraction,
  defocusing, pixel of sensor)
• MTF M(s) of whole system
• Ms M1 M2 M3 M4 very simple!!
• Resolution can be defined v0 from M(?0)0.1

• M(?)

1
M1
M2
M3
0.1
Ms

• ?/Lp/mm

v0
Resolution
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6. Outlook Further topics to be covered in next
months

• Pixel number, pixel size , sensor size (also
  background and noise consideration)
• The MTF formalism (Modulation Transfer Function)
• Calculations with ZEMAX
• TV-system for cathode observation
• Detection efficiency of small signals,background
  and noise, different sources, Noise Equivalent
  Power (NEP) etc.
• Collaboration especially from PhDs wanted

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7. Summary

• A system of switchable lenses is proposed to be
  used instead of a remotely controlled zoom lens
• Several effects limiting the optical resolution
  are discussed
• The correction of the dof problem of inclined
  screens is discussed, solution is offered

• Different effects of optical imaging in the
  measuring process at PITZ should be considered in
  more detail, this is mainly a task for PhD
  students and was a lack in the past. This should
  resuld in detailed corrections and unfolding
• The talk will be continued by a further one
  concerning more detail analysis of optical
  imaging effects and their quantitative analysis.

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• End