Download presentation

Presentation is loading. Please wait.

Published byMiguel Snyder Modified over 4 years ago

1
**Outline Stokes Vectors, Jones Calculus and Mueller Calculus**

Optics of Crystals: Birefringence Common polarization devices for the laboratory and for astronomical instruments Principles of Polarimetry: Modulation and Analysis. Absolute and Relative Polarimetry Principles of Polarimetry: Spatial modulation, Temporal modulation, Spectral modulation Principles of Polarimetry: Noise and errors Spurious sources of polarization

2
**Stokes Vector, Jones Calculus, Mueller Calculus playing around with matrices**

A. López Ariste

3
Assumptions: A plane transverse electromagnetic wave Quasi-monochromatic Propagating in a well defined direction z

4
Jones Vector

5
**Jones Vector: It is actually a complex vector with 3 free parameters**

It transforms under the Pauli matrices. It is a spinor

6
**The Jones matrix of an optical device**

In group theory: SL(2,C)

7
**From the quantum-mechanical point of view, the wave function cannot be measured directly.**

Observables are made of quadratic forms of the wave function: J is a density matrix : The coherence matrix

8
Like Jones matrices, J also belongs to the SL(2,C) group, and can be decomposed in the basis of the Pauli matrices. Is the Stokes Vector

9
**The Stokes vector is the quadractic form of a spinor**

The Stokes vector is the quadractic form of a spinor. It is a bi-spinor, or also a 4-vector

10
**4-vectors live in a Minkowsky space with metric (+,-,-,-)**

11
**The Minkowski space I Partially polarized light Cone of**

(fully polarized) light Fully polarized light V Q

13
**M is the Mueller matrix of the transformation**

14
From group theory, the Mueller matrix belongs to a group of transformations which is the square of SL(2,C) Actually a subgroup of this general group called O+(3,1) or Lorentz group

15
**The cone of (fully polarized) light**

Lorentz boost = de/polarizer, attenuators, dichroism V Q

16
**The cone of (fully polarized) light**

3-d rotation = retardance, optical rotation V Q

17
Mueller Calculus Any macroscopic optical device that transforms one input Stokes vector to an output Stokes vector can be written as a Mueller matrix Lorentz group is a group under matrix multiplication: A sequence of optical devices has as Mueller matrix the product of the individual matrices

18
**Mueller Calculus: 3 basic operations**

Absorption of one component Retardance of one component respect to the other Rotation of the reference system

19
**Mueller Calculus: 3 basic operations**

Absorption of one component

20
**Mueller Calculus: 3 basic operations**

Absorption of one component Retardance of one component respect to the other

22
**Mueller Calculus: 3 basic operations**

Absorption of one component Retardance of one component respect to the other Rotation of the reference system

24
**Optics of Crystals: Birefringence**

A. López Ariste

26
Chapter XIV, Born & Wolf

27
!!

31
Ellipsoïd

32
Ellipsoïd

33
**Three types of crystals**

A spherical wavefront

34
**Three types of crystals**

Two apparent waves propagating at different speeds: An ordinary wave, with a spherical wavefront propagating at ordinary speed vo An extraordinary wave with an elliptical wavefront, its speed depends on direction with characteristic values vo and ve

37
**Three types of crystals**

40
**The ellipsoïd of D in uniaxial crystals**

z s The ellipsoïd of D in uniaxial crystals De The two propagating waves are linearly polarized and orthogonal one to each other Do

42
**Typical birefringences**

Quartz Calcite Rutile Lithium Niobate

43
**Common polarization devices for the laboratory and for astronomical instruments**

A. López Ariste

44
Linear Polarizer

45
Retarder

47
Savart Plate

48
**Glan-Taylor Polarizer**

Glan-Taylor.jpg

49
**Glan-Thompson Polarizing Beam-Splitter**

50
**Rochon Polarizing Beamsplitter**

51
Polaroid

52
**Dunn Solar Tower. New Mexico**

53
**Typical birefringences**

Quartz Calcite Rutile Lithium Niobate Zero-order waveplates Multiple-order waveplates

54
Waveplates

56
**Principles of Polarimetry Modulation Absolute and Relative Polarimetry**

A. López Ariste

57
**How to switch from Measure # 1 to Measure # 2?**

Measure # 1 : I + Q Measure # 2 : I - Q Subtraction: 0.5 (M1 – M2 ) = Q Addition: (M1 + M2 ) = I How to switch from Measure # 1 to Measure # 2? MODULATION

58
**Measure # 1 : I + Q Measure # 2 : I - Q**

Subtraction: 0.5 (M1 – M2 ) = Q Addition: (M1 + M2 ) = I Principle of Polarimetry Everything should be the same EXCEPT for the sign

59
MODULATION

60
MODULATION

61
**O is the Modulation Matrix**

62
**MODULATION Conceptually, it is the easiest thing**

Is it so instrumentally? Is it efficient respect to photon collection, noise and errors?

63
**MODULATION Del Toro Iniesta & Collados (2000)**

Asensio Ramos & Collados (2008) MODULATION

64
**MODULATION Del Toro Iniesta & Collados (2000)**

Asensio Ramos & Collados (2008) Del Toro Iniesta & Collados (2000) MODULATION

65
MODULATION

66
**Design of a Polarimeter**

Specify an efficient modulation scheme: The answer is constrained by our instrumental choices

67
**Absolute vs. Relative Polarimetry**

Efficiency in Q,U and V limited by efficiency in I What limits efficiency in I?

68
**Absolute vs. Relative Polarimetry**

What limits efficiency in I? Measure # 1 : I + Q Measure # 2 : I - Q Subtraction: 0.5 (M1 – M2 ) = Q Addition: (M1 + M2 ) = I Principle of Polarimetry Everything should be the same EXCEPT for the sign

69
**Absolute vs. Relative Polarimetry**

What limits efficiency in I? Measure # 1 : I + Q Measure # 2 : I - Q Subtraction: 0.5 (M1 – M2 ) = Q Addition: (M1 + M2 ) = I Usual photometry of present astronomical detectors is around 10-3 Principle of Polarimetry Everything should be the same EXCEPT for the sign

70
**Absolute vs. Relative Polarimetry**

What limits efficiency in I? Usual photometry of present astronomical detectors is around 10-3 You cannot do polarimetry better than photometry

71
**Absolute vs. Relative Polarimetry**

What limits efficiency in I? Usual photometry of present astronomical detectors is around 10-3 You cannot do ABSOLUTE polarimetry better than photometry

72
**Absolute vs. Relative Polarimetry**

Absolute error : 10-3 I Relative error : 10-3 Q

73
**Absolute vs. Relative Polarimetry**

Li 6708 Absolute error : 10-3 I Relative error : 10-3 Q

75
D2 D1 D2 Phase de 45 deg Phase de 102 deg

76
**Design of a Polarimeter**

Specify an efficient modulation scheme: The answer is constrained by our instrumental choices Define a measurement that depends on relative polarimetry, if a good sensitivity is required

77
**Principles of Polarimetry Spatial modulation, Temporal modulation, Spectral modulation**

A. López Ariste

78
**How to switch from Measure # 1 to Measure # 2?**

Measure # 1 : I + Q Measure # 2 : I - Q Subtraction: 0.5 (M1 – M2 ) = Q Addition: (M1 + M2 ) = I How to switch from Measure # 1 to Measure # 2? MODULATION

79
**How to switch from Measure # 1 to Measure # n?**

80
**Analyser: Calcite beamsplitter**

81
**Analyser: Rotating Polariser**

82
**Analyser: Calcite beamsplitter**

2 beams ≡2 images Spatial modulation Analyser: Rotating Polariser 2 angles ≡ 2 exposures Temporal modulation

83
Modulator: What about U and V?

84
Modulator:

85
Modulator:

86
**Modulator: Rotating λ/4**

87
The basic Polarimeter Modulator Analyzer

88
**Examples QW1 QW2 Measure T1 0° 0 ° Q T2 22.5 ° U T3 -45 ° V T4 45 ° -V**

2 Quarter-Waves + Calcite Beamsplitter QW1 QW2 Measure T1 0° 0 ° Q T2 22.5 ° U T3 -45 ° V T4 45 ° -V ….

89
LCVR Calcite

90
**Examples Rotating Quarterwave plate + Calcite Beamsplitter**

Photelastic Modulators (PEM) + Linear Polariser

91
Spectral Modulation Chromatic waveplate: Followed by an analyzer

92
**See Video from Frans Snik (Univ. Leiden)**

Spectral Modulation Chromatic waveplate: Followed by an analyzer See Video from Frans Snik (Univ. Leiden)

93
**Principles of Polarimetry Noise and errors**

A. López Ariste

94
**Sensitivity vs. Accuracy**

SENSITIVITY: Smallest detectable polarization signal related to noise levels in Q/I, U/I, V/I. RELATIVE POLARIMETRY ACCURACY: The magnitude of detected polarization signal That can be quantiﬁed Parametrized by position of zero point for Q, U, V ABSOLUTE POLARIMETRY

95
**Sensitivity vs. Accuracy**

SENSITIVITY: Smallest detectable polarization signal related to noise levels in Q/I, U/I, V/I. RELATIVE POLARIMETRY Gaussian Noise (e.g. Photon Noise, Camera Shot Noise)

96
**Correcting some unknown errors Spatio-temporal modulation**

Goal: to make the measurements symmetric respect to unknown errors in space and time I+V Detectin in different pixels I-V Exposure 1

97
**Spatio-temporal modulation**

Goal: to make the measurements symmetric respect to unknown errors in space and time I+V I-V Detection at different times Detectin in different pixels I-V I+V Exposure 1 Exposure 2

98
**Spatio-temporal modulation**

I+V I-V I-V I+V Exposure 1 Exposure 2

99
**Spatio-temporal modulation**

Let’s make it more general

100
**Cross-Talk Is this true? This is our polarimeter**

This is what comes from the outer universe Is this true?

103
CrossTalk

105
**Solutions to Crosstalk**

Avoid it: Measure it Mirrors with spherical symmetry (M1,M2) introduce no polarization Cassegrain-focus are good places for polarimeters THEMIS, CFHT-Espadons, AAT-Sempol,TBL-Narval,HARPS-Pol,… Given find its inverse and apply it to the measurements It may be dependent on time and wavelength It forces you to observe the full Stokes vector

106
**Dunn Solar Tower. New Mexico**

108
**Solutions to Crosstalk**

Compensate it Several procedures: Introduce elements that compensate the instrumental polarization Measure the Stokes vector that carries the information Project the Stokes vector into the Eigenvector of the matrix

Similar presentations

Presentation is loading. Please wait....

OK

Polarization Jones vector & matrices

Polarization Jones vector & matrices

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on peak load pricing lecture Ppt on step up transformer Ppt on sri lanka history Pdf to ppt online converter free download Ppt on moving coil galvanometer Ppt on chemical change and physical change Ppt on data collection methods for qualitative research Ppt on regular expression in php Ppt on advertising and brand management Ppt on information technology management