The document summarizes research into using paraxial ray optics to create an optical invisibility cloak. It describes theoretical models for 3-lens and 4-lens cloaking systems. For the 3-lens system, a condition is derived showing cloaking is only possible if the lens focal lengths are very large compared to the distances between them. A 4-lens system is also modeled and shown to satisfy the conditions for a perfect cloak. Experimental setups of the 3-lens and 4-lens cloaks are then described.
Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionizationSérgio Sacani
Within one billion years of the Big Bang, intergalactic hydrogen
was ionized by sources emitting ultraviolet and higher energy
photons. This was the final phenomenon to globally affect all
the baryons (visible matter) in the Universe. It is referred to
as cosmic reionization and is an integral component of cosmology.
It is broadly expected that intrinsically faint galaxies
were the primary ionizing sources due to their abundance
in this epoch1,2. However, at the highest redshifts (z > 7.5;
lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations
to date are intrinsically bright and, therefore, not
necessarily representative of the general population3. Here,
we report the unequivocal spectroscopic detection of a low
luminosity galaxy at z > 7.5. We detected the Lyman-α emission
line at ∼10,504 Å in two separate observations with
MOSFIRE4 on the Keck I Telescope and independently with
the Hubble Space Telescope’s slitless grism spectrograph,
implying a source redshift of z = 7.640 ± 0.001. The galaxy
is gravitationally magnified by the massive galaxy cluster
MACS J1423.8+2404 (z = 0.545), with an estimated intrinsic
luminosity of MAB = −19.6 ± 0.2 mag and a stellar mass of
☆ = × − +
M 3.0 0.8 10
1.5 8 solar masses. Both are an order of magnitude
lower than the four other Lyman-α emitters currently
known at z > 7.5, making it probably the most distant representative
source of reionization found to date.
AUTOMATIC IDENTIFICATION OF CLOUD COVER REGIONS USING SURF ijcseit
Weather forecasting has become an indispensable application to predict the state of the atmosphere for a
future time based on cloud cover identification. But it generally needs the experience of a well-trained
meteorologist. In this paper, a novel method is proposed for automatic cloud cover estimation, typical to
Indian Territory Speeded Up Robust Feature Transform(SURF) is applied on the satellite images to obtain
the affine corrected images. The extracted cloud regions from the affine corrected images based on Otsu
threshold are superimposed on the artistic grids representing latitude and longitude over India. The
segmented cloud and grid composition drive a look up table mechanism to identify the cloud cover regions.
Owing to its simplicity, the proposed method processes the test images faster and provides accurate
segmentation for cloud cover regions.
Spectroscopic confirmation of an ultra-faint galaxy at the epoch of reionizationSérgio Sacani
Within one billion years of the Big Bang, intergalactic hydrogen
was ionized by sources emitting ultraviolet and higher energy
photons. This was the final phenomenon to globally affect all
the baryons (visible matter) in the Universe. It is referred to
as cosmic reionization and is an integral component of cosmology.
It is broadly expected that intrinsically faint galaxies
were the primary ionizing sources due to their abundance
in this epoch1,2. However, at the highest redshifts (z > 7.5;
lookback time 13.1 Gyr), all galaxies with spectroscopic confirmations
to date are intrinsically bright and, therefore, not
necessarily representative of the general population3. Here,
we report the unequivocal spectroscopic detection of a low
luminosity galaxy at z > 7.5. We detected the Lyman-α emission
line at ∼10,504 Å in two separate observations with
MOSFIRE4 on the Keck I Telescope and independently with
the Hubble Space Telescope’s slitless grism spectrograph,
implying a source redshift of z = 7.640 ± 0.001. The galaxy
is gravitationally magnified by the massive galaxy cluster
MACS J1423.8+2404 (z = 0.545), with an estimated intrinsic
luminosity of MAB = −19.6 ± 0.2 mag and a stellar mass of
☆ = × − +
M 3.0 0.8 10
1.5 8 solar masses. Both are an order of magnitude
lower than the four other Lyman-α emitters currently
known at z > 7.5, making it probably the most distant representative
source of reionization found to date.
AUTOMATIC IDENTIFICATION OF CLOUD COVER REGIONS USING SURF ijcseit
Weather forecasting has become an indispensable application to predict the state of the atmosphere for a
future time based on cloud cover identification. But it generally needs the experience of a well-trained
meteorologist. In this paper, a novel method is proposed for automatic cloud cover estimation, typical to
Indian Territory Speeded Up Robust Feature Transform(SURF) is applied on the satellite images to obtain
the affine corrected images. The extracted cloud regions from the affine corrected images based on Otsu
threshold are superimposed on the artistic grids representing latitude and longitude over India. The
segmented cloud and grid composition drive a look up table mechanism to identify the cloud cover regions.
Owing to its simplicity, the proposed method processes the test images faster and provides accurate
segmentation for cloud cover regions.
Noise Removal with Morphological Operations Opening and Closing Using Erosio...IJMER
The mathematical operations are proposed in this paper. By using two mathematical
operations erosion and dilation we can add and remove pixels. We can remove the noise or interference in
power system. Opening and closing operations also discussed with erosion and dilation. These four
morphological operations are also helpful in developing a morphological filter.
Build Your Own 3D Scanner:
Conclusion
http://mesh.brown.edu/byo3d/
SIGGRAPH 2009 Courses
Douglas Lanman and Gabriel Taubin
This course provides a beginner with the necessary mathematics, software, and practical details to leverage projector-camera systems in their own 3D scanning projects. An example-driven approach is used throughout; each new concept is illustrated using a practical scanner implemented with off-the-shelf parts. The course concludes by detailing how these new approaches are used in rapid prototyping, entertainment, cultural heritage, and web-based applications.
POSITION ESTIMATION OF AUTONOMOUS UNDERWATER SENSORS USING THE VIRTUAL LONG B...ijwmn
This article contains a description of a mathematical model of an acoustic system for positioning
autonomous underwater sensors using the virtual long base method, which can be used during the vessel’s
collection of information over the deployed underwater network of autonomous sensors (underwater
wireless sensors network), during the initial determination of the geographical position of the bottom long
baseline elements or search, including cooperative, with the use of a swarm of autonomous surface vehicles
(UASV) of emergency submerged objects equipped with an emergency beacon (for example, aircraft and
ships); The article provides a scheme of an experimental set of equipment, as well as a description of the
conducted field experiments and their results.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Build Your Own 3D Scanner: The Mathematics of 3D TriangulationDouglas Lanman
Build Your Own 3D Scanner:
The Mathematics of 3D Triangulation
http://mesh.brown.edu/byo3d/
SIGGRAPH 2009 Courses
Douglas Lanman and Gabriel Taubin
This course provides a beginner with the necessary mathematics, software, and practical details to leverage projector-camera systems in their own 3D scanning projects. An example-driven approach is used throughout; each new concept is illustrated using a practical scanner implemented with off-the-shelf parts. The course concludes by detailing how these new approaches are used in rapid prototyping, entertainment, cultural heritage, and web-based applications.
A new approach of edge detection in sar images using region based active cont...eSAT Journals
Abstract This paper presents a new methodology for the edge detection of complex radar images. The approach includes the edge improvisation algorithm and followed with edge detection. The nature of complex radar images made edge enhancement part before the edge detection as the data is highly heterogeneous in nature. Thus, the use of discrete wavelet transform in the edge improvisation algorithm is justified. Then region based active contour model is used as edge detection algorithm. The paper proposes the distribution fitting energy with a level set function and neighborhood means and variances as variables. The performance is tested by applying it on different images and the results are been analyzed. Keywords: Edge detection, Edge improvisation, Synthetic Aperture radar (SAR), wavelet transforms.
Noise Removal with Morphological Operations Opening and Closing Using Erosio...IJMER
The mathematical operations are proposed in this paper. By using two mathematical
operations erosion and dilation we can add and remove pixels. We can remove the noise or interference in
power system. Opening and closing operations also discussed with erosion and dilation. These four
morphological operations are also helpful in developing a morphological filter.
Build Your Own 3D Scanner:
Conclusion
http://mesh.brown.edu/byo3d/
SIGGRAPH 2009 Courses
Douglas Lanman and Gabriel Taubin
This course provides a beginner with the necessary mathematics, software, and practical details to leverage projector-camera systems in their own 3D scanning projects. An example-driven approach is used throughout; each new concept is illustrated using a practical scanner implemented with off-the-shelf parts. The course concludes by detailing how these new approaches are used in rapid prototyping, entertainment, cultural heritage, and web-based applications.
POSITION ESTIMATION OF AUTONOMOUS UNDERWATER SENSORS USING THE VIRTUAL LONG B...ijwmn
This article contains a description of a mathematical model of an acoustic system for positioning
autonomous underwater sensors using the virtual long base method, which can be used during the vessel’s
collection of information over the deployed underwater network of autonomous sensors (underwater
wireless sensors network), during the initial determination of the geographical position of the bottom long
baseline elements or search, including cooperative, with the use of a swarm of autonomous surface vehicles
(UASV) of emergency submerged objects equipped with an emergency beacon (for example, aircraft and
ships); The article provides a scheme of an experimental set of equipment, as well as a description of the
conducted field experiments and their results.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Build Your Own 3D Scanner: The Mathematics of 3D TriangulationDouglas Lanman
Build Your Own 3D Scanner:
The Mathematics of 3D Triangulation
http://mesh.brown.edu/byo3d/
SIGGRAPH 2009 Courses
Douglas Lanman and Gabriel Taubin
This course provides a beginner with the necessary mathematics, software, and practical details to leverage projector-camera systems in their own 3D scanning projects. An example-driven approach is used throughout; each new concept is illustrated using a practical scanner implemented with off-the-shelf parts. The course concludes by detailing how these new approaches are used in rapid prototyping, entertainment, cultural heritage, and web-based applications.
A new approach of edge detection in sar images using region based active cont...eSAT Journals
Abstract This paper presents a new methodology for the edge detection of complex radar images. The approach includes the edge improvisation algorithm and followed with edge detection. The nature of complex radar images made edge enhancement part before the edge detection as the data is highly heterogeneous in nature. Thus, the use of discrete wavelet transform in the edge improvisation algorithm is justified. Then region based active contour model is used as edge detection algorithm. The paper proposes the distribution fitting energy with a level set function and neighborhood means and variances as variables. The performance is tested by applying it on different images and the results are been analyzed. Keywords: Edge detection, Edge improvisation, Synthetic Aperture radar (SAR), wavelet transforms.
Crosstalk in misaligned free space optical interconnects: modelling and simul...IJECEIAES
We introduce convenient model and an optimization scheme to optimize the signal-to-crosstalk ratio (SCR) in a free space optical interconnects (FSOIs) system that uses microlenses with finite circular apertures. In this model, we consider both the stray light crosstalk and the crosstalk due to the diffraction at the microlens apertures to evaluate the SCR. Using cylindrical form of Collins diffraction integral and the Laguerre–Gaussian (LG) beam model, we derive an approximate closed form formula for the optical field of a multimode LG beam propagating through circular apertured FSOIs by expanding the hard edge circular aperture function of the microlens in terms of complex Gaussian functions. The analyses indicate that the size of the detector is an important factor to optimize the SCR for both the apertured and the unapertured misaligned FSOIs system. The effect of higher order mode of the laser source on the SCR is also considered.
Electron Diffraction Using Transmission Electron MicroscopyLe Scienze Web News
Electron diffraction via the transmission electron microscope is a powerful method for characterizing the structure of materials, including perfect crystals and defect structures. The advantages of elec- tron diffraction over other methods, e.g., x-ray or neutron, arise from the extremely short wavelength (≈2 pm), the strong atomic scattering, and the ability to exam- ine tiny volumes of matter (≈10 nm3). The NIST Materials Science and Engineer- ing Laboratory has a history of discovery and characterization of new structures through electron diffraction, alone or in combination with other diffraction methods. This paper provides a survey of some of this work enabled through electron mi- croscopy.
Design of a Selective Filter based on 2D Photonic Crystals Materials IJECEIAES
Two dimensional finite differences temporal domain (2D-FDTD) numerical simulations are performed in cartesian coordinate system to determine the dispersion diagrams of transverse electric (TE) of a two-dimension photonic crystal (PC) with triangular lattice. The aim of this work is to design a filter with maximum spectral response close to the frequency 1.55 μm. To achieve this frequency, selective filters PC are formed by combination of three waveguides W 1 K A wherein the air holes have of different normalized radii respectively r 1 /a=0.44, r 2 /a=0.288 and r /a= 0.3292 (a: is the periodicity of the lattice with value 0.48 μm). Best response is obtained when we insert three small cylindrical cavities (with normalized radius of 0.17) between the two half-planes of photonic crystal strong lateral confinement.
Orbital configurations of spaceborne interferometers for studying photon ring...Sérgio Sacani
Recent advances in technology coupled with the progress of observational
radio astronomy methods resulted in achieving a major milestone of astrophysics - a direct image of the shadow of a supermassive black hole, taken
by the Earth-based Event Horizon Telescope (EHT). The EHT was able to
achieve a resolution of ∼20 µas, enabling it to resolve the shadows of the
black holes in the centres of two celestial objects: the supergiant elliptical
galaxy M87 and the Milky Way Galaxy. The EHT results mark the start of a
new round of development of next generation Very Long Baseline Interferometers (VLBI) which will be able to operate at millimetre and sub-millimetre
wavelengths. The inclusion of baselines exceeding the diameter of the Earth
and observation at as short a wavelength as possible is imperative for further development of high resolution astronomical observations. This can be
achieved by a spaceborne VLBI system. We consider the preliminary mission
design of such a system, specifically focused on the detection and analysis
of photon rings, an intrinsic feature of supermassive black holes. Optimised
Earth, Sun-Earth L2 and Earth-Moon L2 orbit configurations for the space
interferometer system are presented, all of which provide an order of magnitude improvement in resolution compared to the EHT. Such a space-borne
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
Expert system of single magnetic lens using JESS in Focused Ion Beamijcsa
This work shows expert system of symmetrical single magnetic lens used in focused ion beam optical system. Java expert system shell(JESS) programming is proposed to build the intelligent agent "MOPTION"for getting an optimum magnetic flux density , and calculate the ion optical trajectory. The combination of such rule based engine and SIMION 8.1 has configured the reconstruction process and compiled the data retrieved by the proposed expert system agent to implement the pole-pieces reconstruction for lens design. The pole pieces reconstruction has been resulted in 3D graph , and under the infinite magnification conditions of the optical path, aberration (spherical / chromatic and total) disks diameters have been obtained and got the values (0.03,0.13 and 0.133) micron (μm) respectively.
Introduction
The applications of microscopy in the forensic sciences are almost limitless. This is due in large measure to the ability of
microscopes to detect, resolve and image the smallest items of evidence, often without alteration or destruction. As a
result, microscopes have become nearly indispensable in all forensic disciplines involving the natural sciences. Thus, a
firearms examiner comparing a bullet, a trace evidence specialist identifying and comparing fibers, hairs, soils or dust, a
document examiner studying ink line crossings or paper fibers, and a serologist scrutinizing a bloodstain, all rely on
microscopes, in spite of the fact that each may use them in different ways and for different purposes.
The principal purpose of any microscope is to form an enlarged image of a small object. As the image is more greatly
magnified, the concern then becomes resolution; the ability to see increasingly fine details as the magnification is
increased. For most observers, the ability to see fine details of an item of evidence at a convenient magnification, is
sufficient. For many items, such as ink lines, bloodstains or bullets, no treatment is required and the evidence may
typically be studied directly under the appropriate microscope without any form of sample preparation. For other types of
evidence, particularly traces of particulate matter, sample preparation before the microscopical examination begins is
often essential. Types of Microscopes Used in the Forensic Sciences
A variety of microscopes are used in any modern forensic science laboratory. Most of these are light microscopes which
use photons to form images, but electron microscopes, particularly the scanning electron microscope (SEM), are finding
applications in larger, full service laboratories because of their wide range of magnification, high resolving power and
ability to perform elemental analyses when equipped with an energy or wavelength dispersive X-ray spectrometer.
AOS is an industry leader in diffractive optics design & manufacturing. We offer the best lens design, metrology, and extensive fabrication of diffractive optical elements with high precision and diffraction efficiency. Visit Us
1. Paraxial Ray Optics Invisibility Cloaking
Tyler Peterson
Pacific Lutheran University
PHYS 499B
21 May 2015
Abstract: Lenses and standard optical components are used to demonstrate a 3-D, transmitting,
passive, continuously multidirectional cloak for objects in the visible light spectrum.
Commercial ray optics software is used to model the cloaking behavior, and a succinct
formalism is presented that yields perfect optical cloaks in the paraxial limit.
2. Introduction
Invisibility cloaking has fascinated both the general public and the scientific community
ever since the idea was first introduced. In 1966, Star Trek screenwriter Paul Schneider unveiled
the first instance of invisibility technology in the episode “Balance of Terror”. The idea came to
him in 1958 after seeing a World War II naval drama, Run Silent, Run Deep, and attempting to
create a space-exploration equivalent to a submerging submarine. The device has since shown up
in countless forms throughout the decades in all mediums of popular media, especially
noticeably in the 1997 novel Harry Potter and the Philosopher’s Stone [4].
Despite its ubiquitous presence in popular culture, optical spatial cloaking has not been
pursued as a scientific endeavor until recent years. Many different approaches have been taken
with varying degrees of success. Advances made in fields like transformation optics have
inspired progress in other fields, and have been showing a gradual shift from traditional
metamaterials, to polymers, and finally to natural materials [2]. To avoid the burden of difficult
materials requirements, researchers have recently turned to ray optics for cloaking [1].
Joseph S. Choi and John C. Howell have been working at the University of Rochester to
develop a cloak that has its foundation in ray optics. The so-called “Rochester Cloak” is
constructed through the careful placement of standard lenses along a central axis to allow an
object to appear invisible from the perspective of a properly placed observer. One of the major
benefits of this system is its multidirectionality; whereas previous attempts at cloaking have been
limited to very specific viewing conditions, this cloak allows an observer to look from a wide
range of incident angles within the paraxial limit (where sin( 𝜃)~tan( 𝜃)~𝜃, valid for incident 𝜃
up to 30°) [1].
3. In this experiment, we work through a reconstruction of two configurations that satisfy
the requirements for a Rochester Cloak. A concise formalism is presented that describes what
takes place in the systems to create the cloaking effect, which is then demonstrated in both a
physical setup and computer simulation. All materials were easily accessible, off the shelf optical
materials, chosen to emphasize the simplicity and effectiveness of this experiment.
Theoretical Formalism
A perfect cloak is defined in this experiment to be any system that satisfies two essential
requirements. First, it must have a non-zero volume of space that is cloaked and available to hide
an object, and second, light rays coming through should be unaltered compared to when the
cloaking system is replaced by the ambient medium [1]. To characterize rays of light as they
move through an optical system, ray transfer matrices are employed.
Optical ray transfer matrices describe how the displacement and slope of an optical ray
changes after passing through a simple optical element. The entries in the matrix characterize the
focusing properties of the element [3].
4. (a)
(b)
Fig. 1. (a) A visual depiction of how a ray transfer matrix represents a ray
entering an optical element (the orange box pictured here) from the “object space”
with a transverse displacement of 𝑟1 and slope 𝑟′1. The ray exits into the “image
space” with an associated transverse displacement 𝑟2 and slope 𝑟′2. (b) A generic
ray transfer matrix representing an incoming ray with transverse displacement 𝑟1
and slope 𝑟′1, and outgoing displacement 𝑟2 and slope 𝑟′2 [3].
The ray matrices for a large number of basic paraxial optical elements can be looked up
easily. The two that will be most useful for this experiment are those for a region of free space
and for a thin lens. Because the Rochester Cloak is comprised of various lenses aligned on a
central axis, these are the only two optical elements present in the system. Hypothetically, any
number of lenses could be chosen and placed in such a way so as to produce a cloaked region,
but for the scope of this research two models were chosen: a three lens cloak, and a four lens
cloak.
1
'
1
2
'
2
r
r
DC
BA
r
r
5. (a) (b)
Fig 2. (a) Ray transfer matrix for free space region with index of refraction n and
total length L. (b) Ray transfer matrix for a thin lens with focal length f [3].
As previously mentioned, a perfect cloak should behave as though it were replaced by the
ambient medium. Synthesizing this with the transfer matrix for an overall system hypothetically
allows for a solvable condition for any arrangement of lenses to form a perfect cloak:
(1)
Before looking at the three or four lens cloaks, the possibility of a two lens cloak was examined.
Ray transfer matrices representing each optical region in a system are multiplied together to yield
the overall transfer matrix. For the two lens system, comprised of two lenses with focal lengths
𝑓1 and 𝑓2, separated by a distance 𝑡, this is given by
[
1 0
−1/𝑓2 1
] [
1 𝑡
0 1
] [
1 0
−1/𝑓1 1
] = [
1 −
𝑡
𝑓1
𝑡
−(𝑓1+𝑓2+𝑡)
𝑓1 𝑓2
1 −
𝑡
𝑓2
] (2)
Equation (1) can only be satisfied if 𝑓1 = 𝑓2 = ±∞, which would essentially collapse the system
into a region of free space, thus eliminating the possibility of any cloaking region or optical
effect.
10
/1 nL
1
1
01
f
10
/1 nL
DC
BA
perfect
6. Fig 3. Three lens cloak system [1].
A three lens system can be represented by the following matrix:
[
1 0
−1/𝑓3 1
] [
1 𝑡2
0 1
] [
1 0
−1/𝑓2 1
] [
1 𝑡1
0 1
] [
1 0
−1/𝑓1 1
] (3)
Carrying through the matrix multiplication and setting C = 0 to satisfy Equation (1) yields the
following condition:
𝑓2 = −
(𝑓1−𝑡1)(𝑓3−𝑡2)
𝑓1+𝑓3−𝑡1−𝑡2
(4)
This substitution simplifies equation (3):
[
𝑓3(𝑓1−𝑡1)
𝑓1(𝑓3−𝑡2)
𝑡1 + 𝑡2 + 𝑡1 𝑡2
(𝑓1+𝑓3−𝑡1−𝑡2)
(𝑓1−𝑡1)(𝑓3−𝑡2)
0
𝑓1(𝑓3−𝑡2)
𝑓3(𝑓1−𝑡1)
] (5)
Since the B entry in the transfer matrix represents overall system length, we can set this
equivalent to the sum of the separation distances to get the following:
(6)
This equation illuminates the fatal flaw of the three lens configuration: this equation only holds if
𝑡1 = 0, 𝑡2 = 0,or (𝑓1 + 𝑓3 − 𝑡1 − 𝑡2) = 0. The first two cases yield a two lens system which has
0
))((
)(
2311
2131
21
tftf
ttff
tt
7. been shown to be ineffective. The third requires that 𝑓2 → ∞, which again turns the system into a
two lens configuration.
Although this result tells us that a three lens cloak can never satisfy the requirements of a
perfect cloak, considering a symmetric case yields an interesting outcome. Looking at the setup
where 𝑓1 = 𝑓3 and 𝑡1 = 𝑡2, the following condition becomes apparent.
(7)
Therefore, the system asymptotically approaches a perfect cloak for 𝑓1 ≫ 𝑡1. This symmetric
setup also alters equation (4) after setting A = 1 and C = 0 to satisfy equation (1):
(8)
The setup of the four lens cloak follows a very similar process of manipulating the system’s
ray transfer matrix to look like the free space matrix. The guiding philosophy for this cloak is to
undo any changes that the first half of the system makes with the second half. To accomplish
this, a symmetric cloak is considered where 𝑓1 = 𝑓4, 𝑓2 = 𝑓3, and 𝑡1 = 𝑡3. Constructing the ray
transfer matrix in similar fashion to the two and three lens systems, we get
(9)
0
2
11
2
1
tf
t
121 2 fft
1/1
01
10
1
1/1
01
10
1
1/1
01
10
1
1/1
01
1
1
2
2
3
3
4 f
t
f
t
f
t
f
8. Fig 4. Four lens cloak system [1].
After matrix multiplication and setting A = 1 and C = 0 as mandated by the perfect cloak matrix,
we find the spacing condition for the first and third displacements:
(10)
We obtain our final separation condition by setting the total length of the system equivalent to
the sum of the separation distances:
(11)
These conditions provide an exact solution to equation (1) and thus a perfect cloak
comprised of four lenses. The major benefit of both of these cloaking systems is that they are set
up proportionally to the focal lengths of the lenses. Because of this, a variety of different set ups
can be tested to optimize the system and allow for a more widely applicable device.
Experimental Setup
The three lens cloak was set up with two converging lenses on either end and one
diverging lens placed in the middle. The focal length of the first and third lenses was determined
to be 130mm ± 5mm. The middle lens was determined to have a focal length of -40mm ± 12mm.
From these lengths, the separation distance was then calculated to be 50mm ± 13mm.
211 fft
21
212
2
)(2
ff
fff
t
9. Fig 5. Ray trace diagram made with OpticalRayTracer 8.9 to illustrate the
cloaking effect of the three lens cloak. The blacked out regions represent the
cloaking region. The overall cloaked region is a solid of revolution with the black
isosceles triangles in the above cross-sectional slice as the generating shapes,
observable when viewing the system on-axis through the first lens [5].
(a) (b)
Fig 6. (a) Side view of experimental setup of three lens cloak. (b) Observer’s
perspective of system. Graph paper demonstrates the lack of background
distortion, the primary goal of a perfect cloak
10. The four lens cloak was setup with two pairs of converging lenses with equivalent focal
lengths. The first and fourth lenses were measured to have focal lengths of 200mm ± 5mm, and
the second and third lenses were measured to have focal lengths of 51mm ± 5mm. From these,
the first and third separation distances were calculated to be 250mm ± 10mm, and the middle
separation distance to be 170mm ± 22mm.
Fig 7. OpticalRayTracer 8.9 simulation of four lens cloak to illustrate cloaking
region. Again, the blacked out region represents a cross-sectional slice of the
region that would appear cloaked to an observer [5].
11. (a)
(b)
Fig 8. (a) Side view of four lens cloak setup. The ruler is placed at the position of
greatest cloaking, seen as the point of convergence of the incoming light rays
between the first and second lenses in Fig. 7. (b) Observer’s perspective of cloak,
demonstrating the cloaking effect on a ruler.
12. Conclusion
The theoretical framework for this experiment provided systems of equations that
describe the parameters for both a three and four lens cloak. While the three lens system only
approximated a perfect cloak, the four lens system exactly matched the requirements. These
results are not without their limitations, however. Aberrations were noticeable in the background
when looking through the cloak in both cases. The graph paper was chosen specifically to
illustrate how effectively these cloaking systems left the background unaltered, but upon
inspection there were slight distortions and blurs. These can be attributed to uncertainty in the
focal lengths and separation distances, as well as imperfections in the materials in the lenses. The
uncertainty in the middle diverging lens in the three lens cloak is the greatest out of all the
materials on hand. This uncertainty came from some difficulty that arose in determining the final
image distance in the focal length measurement, leaving the placement of this lens up to question
for the working demonstration. Human error in attempting to align the lenses all along a central
axis could also have contributed. Along these same lines, the coating and materials used in the
production of lenses can affect the properties of the cloak [1]. Another limitation of the
Rochester Cloak is the presence of edge effects; if an observer views the cloak from too close,
there is a substantial amount of unwanted rays on the outside of the cloaking region, outside the
paraxial limit.
This is an exciting experiment because it offers a vast array of options for future research.
Because the nature of the Rochester Cloak is such that it can scale to any size given the proper
materials, much of this future research would revolve around optimization. One major goal
would be the reduction of edge effects, as well as achieving a larger field-of-view for an
observer. These could be attained by working not just with different focal lengths and separation
distances, but also lens diameters. Work could also be done towards making the cloaking region
13. more independent of incident ray angles. A final suggestion for future research would be to
pursue new lens configurations. One might allow for cloaking of the center region, whereas these
designs cloaked solids of revolution, leaving the center region visible. Also, there could be non-
symmetric solutions to these cases that were left unexplored in this experiment.
In summary, this experiment defined what conditions need to be met in order to create a
perfect cloak and then offered a three lens system that approximated these conditions, and a four
lens system that exactly matched them. Experimental demonstrations were assembled to
illustrate the cloaking effect predicted by the theoretical framework, which were then simulated
using OpticalRayTracer 8.9. This project provides a formalism which can effectively describe
ray optics invisibility cloaking.
References
[1] Choi, J.S., J. C. Howell, “Paraxial Ray Optics Cloaking,” Optics Express 22, (2014).
[2] Howell, J. C., J. B. Howell, J. S. Choi, “Amplitude-Only, Passive, Broadband, Optical Spatial
Cloaking of Very Large Objects,” Applied Optics 53, 1958-63 (2014).
[3] Siegman, Anthony E. “Lasers,” University Science Books (1986).
[4] "A Brief History of the Real-life Invisibility Cloak." A Brief History of the Real-life
Invisibility Cloak. 27 Mar. 2013. Web. 19 May 2015. <http://theweek.com/articles/466216/brief-
history-invisibility-cloak>.
[5] P. Lutus, (2015), WWW Document, (http://arachnoid.com/OpticalRayTracer/).