Prof. Jose Sasian
Diffractive Optical Elements
Lens Design OPTI 517
Prof. Jose Sasian
Diffractive Lenses
What they are
How they work
Zone spacing and blaze profile roles
First order properties
Dispersion
Two point construction model
Phase model
Sweatt
model
Efficiency
Diffractive landscape lens
Prof. Jose Sasian
Terminology
Diffractive optical element: generic term
Fresnel lens: Scale of zones and lack of organized phasing
Kinoform: Phased Fresnel lens. Phase modulation from surface relief
Holographic optical element: Produced by interfering two or more
beams
Binary optics: Made by staircases that approximate the ideal surface relief
Fresnel zone plate: A particular pattern that produces amplitude
modulation.
Hybrid lens: combined refractive and diffractive power
Computer generated hologram: A hologram produced by calculations in a computer
Prof. Jose Sasian
The work of a diffractive optical element
Organized rearrangement of the wavefront
Prof. Jose Sasian
Fresnel Lens
A Fresnel lens reduces the amount of bulk glass.Scale of zones is large and the wavefront segments are not rearranged to re-create
a spherical wavefront. The ring-zone segments is not properly organized.
mm
Prof. Jose Sasian
Two contexts for DOE: amplitude and phase
Blaze determines amplitude of diffracted ordersGeometry of zone boundary determines wavefront shape (phase)
The wavefront deformation introduced by a DOE is equal to thewavefront deformation represented by the DOE when it is thought
ofas an interferogram
Prof. Jose Sasian
Example
Straight fringes represent tilt and so the beam is deviated
Prof. Jose Sasian
Example
Circular fringes represent defocus and so a DOE with these zone boundaries will introduce optical power
Depending on the spacing, spherical aberration can also be introduced
Prof. Jose Sasian
An infrared DOE
From Michael Morris
Prof. Jose Sasian
A Fresnel lens cut-away
Prof. Jose Sasian
First-order properties2 2
2 2 2 2 22n
n
f r f n
f r f nf n
f
2nr nf
r Given a focal length the zoneboundaries are defined.The optical path differenceBetween zones isone wavelength
Prof. Jose Sasian
Paraxial diffractive lens definition
2nr nf
Prof. Jose Sasian
Zone Spacing
2
2 21 1 1
2
2 2
2 / #2
n
n n n n n n n
micrometersn
r nf
r r r r r r r dr ffSpacing dr Fr
Prof. Jose Sasian
Focal length for a given spacing
0n construction construction
construction reconstruction reconstruction
r drf f
constructionDesigned for
Used at reconstruction
Prof. Jose Sasian
Prof. Jose Sasian
Diffractive V-number1
1 1f c f c
d d refractive
n n n nrn r n
/ 1 1/ 3.5
f c f c
d d diffractive
m dym d y
'sin ' sin mn nd
'y
1
sin ' /y yf
m d
Prof. Jose Sasian
Diffractive focal length from grating perspective
0
1sin ' /
/construction
construction reconstruction
construction
reconstruction
y yfm d
ym d
f
Prof. Jose Sasian
Modeling Diffractive Optics
Two point construction model
Phase function
Sweatt
model
Prof. Jose Sasian
Two point construction model
tionreconstruconconstructim ,,
tionreconstruconconstructim ,,
),,( ZYXA
tionreconstruconconstructim ,, ),,( ZYXB
Prof. Jose Sasian
Phase model
.....2 8642 dcba22 yx
Prof. Jose Sasian
Phase model
Prof. Jose Sasian
Sweatts
model 1n
For n~10,000 alpha must be very small to maintain The same deviation
1nr
For a plano convex lens with n~10,000The radius must be very long to maintainThe same optical power.
Prof. Jose Sasian
(1/d)
Prof. Jose Sasian
Sweatts
Model
(1/d)
Prof. Jose Sasian
Dispersion in Sweatts
model
1
' 1
' '
1 10,0003.5
10,000 10,000
d
F C F C
d d drefractive
F C F C F C
n
Sin I Sin I n
Sin I Sin I n n
nn n
Prof. Jose Sasian
Dispersion in Sweatts
model
Schott: n()
= A+B +
'
' '
dd d
F CF C
d
drefractive
F C F C
mSin I Sin Id
Sin I Sin I md
md
md
Consistent with diffraction case
Prof. Jose Sasian
Structural coefficients: Thin lens (stop at lens)
DCYBXYAXySI 223441
2 212II
S y EX FY
2IIIS
2 1IVS n
0VS
12yCL
0TC
212
nnnA
22
1nnD
1
14
nnnB
11
nnnE
nnC 23
nnF 12
12
12
21
21
rrrr
cccc
X
uuuu
mmY
''
11
))(1( 1 xccncn
Prof. Jose Sasian
Diffractive lens (n very large @ X=0)
23 1I Y 2II Y
1III
0IV
0V 1
Ldiffractive
0T C=3; D=1; F=2
Prof. Jose Sasian
Aberration coefficients for Y=1; X=0
For general case one needs to be careful as the shape dependson the index for a given power.
22
20
IIyS f
2
0III
Sf
Prof. Jose Sasian
Structural coefficients for diffractive lens
2
222
4 8 3 1IY YRR
2
2 2II YR
1III
0IV 0V
1L
diffractive
0T
Prof. Jose Sasian
Field curvature correction hybrid lens
Prof. Jose Sasian
Verification
Prof. Jose Sasian
OPD Alternate view
OPD has two parts. One is due to material dispersion, the other to due to diffraction
2
2
2
2
2
1 12
1 12
1 12
12
1 12
FF F d
d
FF C F d
d
CC d
d
F CF C d
d
ref diff
yOPD n nR
yOPD OPD n nR
y n nR
y n n nR
y
OPD n t N
Prof. Jose Sasian
Spherical aberration
Depending on the zone boundary distribution DOE axially symmetric DOE can introduce different orders of spherical aberration
.....2 8642 dcba
Prof. Jose Sasian
Calculating order efficiency
Simple case of an amplitude device with a square wave profile
Duty cycle
0, **pxx y A Comb x nx rectd
m=0m=1m=2
Prof. Jose Sasian
Square wave
0
0 0 0 0
0 0 0
0 00
2
2 2 2 3 2 3
2 5 2 5 2 7 2 7
2 2 2 2
2 2
2 3
5 7
i n t
i n t i n t i n t i n t
i n t i n t i n t i n
A A nF SINC n SINC n
A nf t square wave SINC e
A A Ae e e e
A Ae e e e
0
10
...t
T
50% duty cycle
21 0.1
Prof. Jose Sasian
Binary optics technology
Prof. Jose Sasian
Efficiency for binary optics
Prof. Jose Sasian
Efficiency
2 2 1 212 2 22 3
11
2 222 2
22
1 1 1 11 1 12 2 3 3
11 2
1 4 1 113 4 12
113
2 ; 0.174 ; 0.7948 ; 0.94816 ; 0.987
hx h hn dx n x nN N N
hn h
hnN N
SN
N SN SN SN S
h/N
h
221S
Prof. Jose Sasian
Efficiency
mnnc
onconstructi
tionreconstruc
tionreconstruc
onconstructi
11sin 2
Prof. Jose Sasian
Efficiency222 21 1
3reconstruction construction
reconstruction
onconstructitionreconstruc
Prof. Jose Sasian
Comparison Standard lens, Fresnel lens and DOE lens
Refracting lens Fresnel lens DOE lens
Prof. Jose Sasian
Images of extended objects
Acrylic powerless lens
Other orders produce images at different magnificationsLike ghost images
Prof. Jose Sasian
Canons multilayer DOEs
Prof. Jose Sasian
How does it work?
Prof. Jose Sasian
How does it work?
2 1sin
1reconstructionconstruction
reconstruction construction
nc m
n
2 21sin sinreconstruction constructionreconstruction reconstruction
n dc d m c md
2 122 1
2 2 1 1
1 1sin
1 1
reconstruction reconstruction
reconstruction reconstruction
reconstruction reconstruction reconstruction
n nc d d m
or d n d n
Prof. Jose Sasian
100% at two wavelengths
Prof. Jose Sasian
Alternate view 100% efficiency at 2
(no ripple)
2 12 2 450nm
Prof. Jose Sasian
An actual lens application for controlling chromatic change of magnification
Note lack of lens symmetry about the stop
DOE
Prof. Jose Sasian
Plastic Fresnel lens; Diamond turned and replicated Gray scale; note binary edge
Binary 16 levelsBinary 8 levels
Some Fresnel lens and DOE photographs
Prof. Jose Sasian
Measurement of a DOE
Prof. Jose Sasian
Beware
Modeling assumes DOEs
having no physical structure
Real modeling faces sampling issues
Scal