the composite ray matrix for an imaging system · the composite ray matrix for an imaging system...
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If
then
The composite ray matrix for an imaging system
AND
If
then
The composite ray matrix for an imaging system
AND
THUS
A lens is a device that maps a point emitter in the object plane at d1 to a point in the image plane at d2
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
What is the sign of R?
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
What is the sign of R?
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Recall for a Gaussian Beam
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
What is the sign of R?
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Recall for a Gaussian Beam
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
What is the sign of R?
Convention: curvature positive if source to the left
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Recall for a Gaussian Beam
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
2i) The image equaLon implies that a spherical wave with a parLcular origin and radius of curvature hiQng the lens is transformed to a new spherical wave with a different radius of curvature and origin. Write down the transformaLon law for the radii of curvature. BEWARE THE SIGN OF R !
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
2i) The image equaLon implies that a spherical wave with a parLcular origin and radius of curvature hiQng the lens is transformed to a new spherical wave with a different radius of curvature and origin. Write down the transformaLon law for the radii of curvature. BEWARE THE SIGN OF R !
2j) Given q’s relaLon to R derive the transformaLon law for a Gaussian beam q-‐parameter
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) The image equaLon implies that a spherical wave with a parLcular origin and radius of curvature hiQng the lens is transformed to a new spherical wave with a different radius of curvature and origin. Write down the transformaLon law for the radii of curvature. BEWARE THE SIGN OF R !
2j) Given q’s relaLon to R derive the transformaLon law for a Gaussian beam q-‐parameter
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
2i) The image equaLon implies that a spherical wave with a parLcular origin and radius of curvature hiQng the lens is transformed to a new spherical wave with a different radius of curvature and origin. Write down the transformaLon law for the radii of curvature. BEWARE THE SIGN OF R !
2j) Given q’s relaLon to R derive the transformaLon law for a Gaussian beam q-‐parameter
Lens focal length: f
A lens is a device that maps a point emitter in the object plane at do to a point in the image plane at di
Image equation
2i) Given (2h) what can you say this system does to transform a spherical wave? Draw it! Bonus) What does this system do to a the q-‐parameter of a Gaussian beam?
2i) The image equaLon implies that a spherical wave with a parLcular origin and radius of curvature hiQng the lens is transformed to a new spherical wave with a different radius of curvature and origin. Write down the transformaLon law for the radii of curvature. BEWARE THE SIGN OF R !
2j) Given q’s relaLon to R derive the transformaLon law for a Gaussian beam q-‐parameter
A lens is a device that transforms a Gaussian q-parameter according to
A general optical system transforms q as
OR
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
recall
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
recall
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
BUT we need
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
BUT we need So divide all terms by f
lens
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
lens
recall
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
lens
recall
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
A lens is a device that transforms a Gaussian q-parameter according to
3a) Find the ABCD values for the lens.
A general optical system transforms q as
OR
3b) What does propagaLon in free space thru a distance d do to the q-‐parameter?
3c) Find the ABCD values for free space propagaLon thru distance d
lens
distance
recall
the imaginary parts are equal !
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
Image from Fundamentals of Photonics 2nd EdiLon by Bahaa E. A. Saleh & Malvin Carl Teich
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall BONUS : What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall
using Ideal minimum spot size
What happens as z0 << f ?
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall What happens as z0 << f ?
using Ideal minimum spot size
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall What happens as z0 << f ?
using Ideal minimum spot size
The input beam is AT ITS FOCUS, so q is purely imaginary
3d) Suppose a lens is placed at the focus of a Gaussian beam. Sketch the situaLon. What is the q-‐parameter before and aYer the lens? Describe where and what is the minimum width of the beam aYer the lens in the limit of z0 >> f.
recall What happens as z0 << f ?
The lens does nothing…
using Ideal minimum spot size
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