the composite ray matrix for an imaging system · the composite ray matrix for an imaging system...
TRANSCRIPT
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