| 1. |
- Burvall, Anna, 1976-
(författare)
-
Axicon imaging by scalar diffraction theory
- 2004
-
Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Axicons are optical elements that produce Bessel beams,i.e., long and narrow focal lines along the optical axis. Thenarrow focus makes them useful ine.g. alignment, harmonicgeneration, and atom trapping, and they are also used toincrease the longitudinal range of applications such astriangulation, light sectioning, and optical coherencetomography. In this thesis, axicons are designed andcharacterized for different kinds of illumination, using thestationary-phase and the communication-modes methods. The inverse problem of axicon design for partially coherentlight is addressed. A design relation, applicable toSchell-model sources, is derived from the Fresnel diffractionintegral, simplified by the method of stationary phase. Thisapproach both clarifies the old design method for coherentlight, which was derived using energy conservation in raybundles, and extends it to the domain of partial coherence. Thedesign rule applies to light from such multimode emitters aslight-emitting diodes, excimer lasers and some laser diodes,which can be represented as Gaussian Schell-model sources. Characterization of axicons in coherent, obliqueillumination is performed using the method of stationary phase.It is shown that in inclined illumination the focal shapechanges from the narrow Bessel distribution to a broadasteroid-shaped focus. It is proven that an axicon ofelliptical shape will compensate for this deformation. Theseresults, which are all confirmed both numerically andexperimentally, open possibilities for using axicons inscanning optical systems to increase resolution and depthrange. Axicons are normally manufactured as refractive cones or ascircular diffractive gratings. They can also be constructedfrom ordinary spherical surfaces, using the sphericalaberration to create the long focal line. In this dissertation,a simple lens axicon consisting of a cemented doublet isdesigned, manufactured, and tested. The advantage of the lensaxicon is that it is easily manufactured. The longitudinal resolution of the axicon varies. The methodof communication modes, earlier used for analysis ofinformation content for e.g. line or square apertures, isapplied to the axicon geometry and yields an expression for thelongitudinal resolution. The method, which is based on abi-orthogonal expansion of the Green function in the Fresneldiffraction integral, also gives the number of degrees offreedom, or the number of information channels available, forthe axicon geometry. Keywords:axicons, diffractive optics, coherence,asymptotic methods, communication modes, information content,inverse problems
|
|
| 2. |
- Burvall, Anna, et al.
(författare)
-
Communication modes applied to axicons
- 2004
-
Ingår i: Optics Express. - 1094-4087. ; 12:3, s. 377-383
-
Tidskriftsartikel (refereegranskat)abstract
- The communication modes, which constitute a convenient method for the propagation and information analysis of optical fields, are formulated in the generalized axicon geometry. The transmitting region is the axicon’s annular aperture, and the observation domain is the optical axis containing the focal line segment. We show that in rotational symmetry one may employ the prolate spheroidal wave functions to represent the communication modes. Further, in usual circumstances the modes can be approximated by quadratic waves in the aperture domain and by sinc functions in the image domain. Both the exact communication modes and the approximate technique are confirmed numerically, with linear axicons as examples.
|
|
| 3. |
- Burvall, Anna, 1976-, et al.
(författare)
-
Communication modes for information content analysis
- 2004
-
Ingår i: LFNM 2004. - : IEEE conference proceedings. - 0780384296 ; , s. 112-114
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Approximate modes which give physical understanding for the communication modes theory,are discussed. For the geometry consisting of two line or square apertures, perpendicular to the optical axis, this approximation leads to exactly the same modes as Gabor's theory would yield.
|
|
| 4. |
- Burvall, Anna, et al.
(författare)
-
Communication modes in axicon imaging
- 2004
-
Ingår i: Riao/Optilas 2004: 5th Iberoamerican Meeting On Optics And 8th Latin American Meeting On Optics, Lasers, And Their Applications, Pts 1-3: Ico Regional Meeting. - : SPIE. - 081945575X ; , s. 1133-1137
-
Konferensbidrag (refereegranskat)abstract
- The communication modes are an increasingly frequently used technique for studying the radiation, propagation, and scattering of light. The method is unusual in the way that it gives the information content and the resolution of the fields. It also allows for the possibility of including the noise considerations in the calculations. We present a brief summary of the communication modes method, together with our latest contribution: the communication modes for the axicon geometry.
|
|
| 5. |
- Burvall, Anna, et al.
(författare)
-
Communication modes in large-aperture approximation
- 2007
-
Ingår i: Optics Letters. - 0146-9592 .- 1539-4794. ; 32:6, s. 611-613
-
Tidskriftsartikel (refereegranskat)abstract
- Simplified versions of the communication modes in the Fresnel domain are derived when the system apertures are large. The approximate modes, which are in the form of spherical waves and sinc functions with a spherical curvature, give physical insight into the communication modes approach and the basic limits of free-space optical communication systems. They also show that Gabor's information theory is readily derived from the communication modes.
|
|
| 6. |
- Burvall, Anna, 1976-, et al.
(författare)
-
Diffraction analysis of lens axicons
- 2005
-
Ingår i: Diffractive Optics 2005. - : European Optical Society. ; , s. 1-2
-
Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Axicons, as shown in Fig. 1(a), are optical elements that produce long and narrow focallines along the optical axis, rather than the conventional focal point created by a lens. Thefocal line can be used for e.g. alignment, extending the focal depth of existing methods, orparticle trapping and transportation. Axicons are mainly produced as refractive glass cones,or as di®ractive gratings consisting of concentric circles. They can also be constructed fromordinary lenses or lens systems, referred to as lens axicons. There are several lens axicondesigns, using spherical or aspheric surfaces to produce the necessary amount of sphericalaberration.
|
|
| 7. |
- Burvall, Anna, 1976-, et al.
(författare)
-
Elementary functions : Propagation of partially coherent light
- 2009
-
Ingår i: Journal of the Optical Society of America A. - : Optical Society of America. - 0740-3232. ; 26:7, s. 1721-1729
-
Tidskriftsartikel (refereegranskat)abstract
- The theory of propagation of partially coherent light is well known, but performing numerical calculations still presents a difficulty because of the dimensionality of the problem. We propose using a recently introduced method based on the use of elementary functions [Wald et al. Proc. SPIE6040, 59621G (2005)] to reduce the integrals to two dimensions. We formalize the method, describe its inherent assumptions and approximations, and introduce a sampling criterion for adequate interpolation. We present an analysis of some special cases, such as the Gaussian Schell-model beam, and briefly discuss generalized numerical propagation of two-dimensional field distributions.
|
|
| 8. |
- Burvall, Anna, 1976-, et al.
(författare)
-
Lens axicons in oblique illumination
- 2007
-
Ingår i: Applied Optics. - : Optical Society of America. - 1559-128X .- 2155-3165. ; 46:3, s. 312-318
-
Tidskriftsartikel (refereegranskat)abstract
- Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.
|
|
| 9. |
- Burvall, Anna, 1976-, et al.
(författare)
-
Linearity of the pyramid wavefront sensor
- 2006
-
Ingår i: Optics Express. - : Optical Society of America. - 1094-4087. ; 14:25, s. 11925-11934
-
Tidskriftsartikel (refereegranskat)abstract
- The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory. We also show that geometrical, diffraction and experimental results are very similar, and conclude that the approximate geometrical predictions can be used in place of the more complex diffraction results.
|
|
| 10. |
- Burvall, Anna, et al.
(författare)
-
Phase retrieval in X-ray phase-contrast imaging suitable for tomography
- 2011
-
Ingår i: Optics Express. - 1094-4087. ; 19:11, s. 10359-10376
-
Tidskriftsartikel (refereegranskat)abstract
- In-line phase-contrast X-ray imaging provides images where both absorption and refraction contribute. For quantitative analysis of these images, the phase needs to be retrieved numerically. There are many phase-retrieval methods available. Those suitable for phase-contrast tomography, i.e., non-iterative phase-retrieval methods that use only one image at each projection angle, all follow the same pattern though derived in different ways. We outline this pattern and use it to compare the methods to each other, considering only phase-retrieval performance and not the additional effects of tomographic reconstruction. We also outline derivations, approximations and assumptions, and show which methods are similar or identical and how they relate to each other. A simple scheme for choosing reconstruction method is presented, and numerical phase-retrieval performed for all methods.
|
|
