Demonstration of a Fresnel axicon Kevin Gourley,1 Ilya Golub,1,* and Brahim Chebbi2,3 1
School of Advanced Technology, Algonquin College, Ottawa, Ontario K2G 1V8, Canada 2
School of Engineering, Laurentian University, Sudbury, Ontario P3E 2C6, Canada 3
e-mail:
[email protected]
*Corresponding author:
[email protected] Received 23 September 2010; revised 28 November 2010; accepted 29 November 2010; posted 3 December 2010 (Doc. ID 135528); published 14 January 2011
We design and manufacture a Fresnel axicon (fraxicon) that generates a quasi-diffraction-free/Bessel beam with a large depth of field. The novel optical element is characterized with both coherent and incoherent light, and its behavior is compared with that of a classical axicon. While the fraxicon exhibits a strong interference pattern in the on-axis intensity distribution, it can be smoothed out when using broadband light, partial spatial coherence light, or by period randomization. As inexpensive, compact/lightweight, and low-absorption elements, fraxicons may find applications in imaging, illumination, and situations where low absorption and dispersion are important. © 2011 Optical Society of America OCIS codes: 220.0220, 070.3185, 120.0120, 230.0230.
An axicon [1,2] is, energywise, the most efficient method for producing a quasi-nondiffracting or zero-order Bessel-type beam [3] that preserves its transverse distribution along the optical axis for distances much larger than the Rayleigh range. The increase of depth of field/focal range, in addition to being a major thrust in the development of modern imaging, is important in metrology/alignment, illumination, and laser machining [4]. Different types of axicons have been proposed, mainly to modify longitudinal intensity distribution [5,6] or to increase resolution [7]. Recently, we put forward the idea of a Fresnel axicon (fraxicon) [8] (Fig. 1), which incorporates the principles of Fresnel lenses into axicon procurement and bridges the gap between refractive and diffractive axicons. The advantages of a fraxicon include compactness, low absorption, and simplicity/inexpensiveness in manufacturing. While preliminary results on a fraxicon were reported in Ref. [9], the main characteristics of the generated quasi-diffraction-free/Bessel beam were not presented. The aim of the present work is to compare the properties of the fraxicon to those of a classical, or 0003-6935/11/030303-04$15.00/0 © 2011 Optical Society of America
linear, axicon in order to find the fraxicon limitations, thus enabling us to determine the applications most suitable for the new element. Both the fraxicon and the classical reference axicon (against which we compare the novel element) were manufactured by B-Con Engineering, Inc., using diamond turning of a plastic material (Zeon E48R), with n ¼ 1:52. Both components had the same 5° base angle and 25:4 mm diameter. For the axicon, a sag of z ¼ r · tan 5° was used, while the fraxicon had a 200 μm periodic structure, with a sag given by zm ¼ ½rm − 200ðm − 1Þ · tan 5° and 200ðm − 1Þ ≤ rm < 200 m with m an integer. The fraxicon is 0:8 mm thick, while the axicon is ∼2 mm thick at the vertex. In our experiments, we used a 0:543 μm He–Ne laser beam expanded telescopically 12× to a beam diameter (1=e2 value) of 2ω ¼ 10:3 mm as well as a white light (∼200 nm FWHM) source (Thorlabs OSL1). For the incoherent light, a 50 μm aperture at the source was used, and the beam was collimated to a nearly plane wave (for smaller apertures, the intensity was too small to obtain quantitative measurements). A 20× microscope objective was used to enlarge the central spot while measuring the 20 January 2011 / Vol. 50, No. 3 / APPLIED OPTICS
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Fig. 1. Bulk axicon and an equivalent fraxicon.
on-axis intensity and recording the lateral intensity distributions. The transverse intensity distributions for both the fraxicon and the classical axicon illuminated by a laser were taken with a CCD camera and are shown in Figs. 2(a) and 2(b) with a 100 μm calibration scale. The photographs (and the subsequent ones in the paper) were overexposed to make the secondary maxima more visible; for quantitative measurements, care was taken to have a linear response. Figure 3 shows the measured transverse intensity distribution of the quasi-nondiffracting beams generated by the fraxicon and the axicon at three different distances of 1, 4, and 8 cm from the optical component. We can see that the transverse distributions are very similar for both elements. The radius of the Bessel/ nondiffracting beam (the distance from the maximum to the first minimum) is given by r0 ¼
1:22λ ; π sin β
ð1Þ
where β ¼ arcsinðn · sin αÞ − α, α being the base angle of the axicon and n being the refractive index of the material. From the measured angle β for both elements, we calculate the spot size (2r0 ) to be 9 and 8:8 μm for the fraxicon and axicon, respectively. The measured values are 9:78 mm and 8:66 μm, correspondingly. The larger discrepancy between the theoretical and measured (larger) value for the fraxicon can be attributed to the light scattering from the
Fig. 3. (Color online) Transverse intensity distributions of beams produced by (a) classical axicon and (b) fraxicon at three different positions on the optical axis of 1 cm (top), 4 cm (middle) and 8 cm (bottom).
edges, diffraction, manufacturing errors, and stressinduced deformation in the thin (0:8 mm) fraxicon, causing broadening of the spot. Next we measured the longitudinal intensity distribution for a fraxicon and a classical axicon illuminated by a laser (Fig. 4). The beats for the fraxicon case are due to diffraction by a long period structure (in addition to diffraction of an apertured beam, as in the case of an axicon) and/or from the dark/shadow segments in the fraxicon-produced focal line [8–10]. These fringes are quite dominant and can be detrimental in many applications. However, they can be
Fig. 2. (Color online) Photographs of quasi-Bessel-type beams produced by (a) classical axicon and (b) fraxicon with a calibration scale. 304
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Fig. 4. Measured on-axis intensity distributions of beams produced by an axicon and a fraxicon for a laser source.
Fig. 5. Measured on-axis intensity distributions of beams produced by a fraxicon and an axicon for a white light source.
suppressed by randomization of the interfacet distance, as was suggested and shown experimentally in Ref. [11] for Fresnel lenses, or by using partial spa-
tial coherence light [12]. Moreover, these interference fringes can be eliminated when using a white light source [13,14]. Figure 5 presents the measured
Fig. 6. (Color online) Ring pattern and ring profile in the vicinity of the focal ring generated by combinations of (a) lens-axicon and (b) lens-fraxicon. 20 January 2011 / Vol. 50, No. 3 / APPLIED OPTICS
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to other optical elements/systems such as logarithmic axicons [5], exicons [6], and the combination of three axicons [20]. This work was supported by an Ontario Centers of Excellence grant. References
Fig. 7. (Color online) Fraxicon-lens combination generated ring pattern with a calibration scale.
longitudinal intensity distribution for both elements with a white light source illumination. Here we used a beam whose central part of ∼12 mm diameter is a plane wave; thus, the measurements were performed and are presented just for on-axis intensity produced by this beam part. The curve is smooth when using this source for both components (note that the final divergence/spatial coherence of such a source facilitates the elimination of the shadow regions of the fraxicon). This possibility of smoothing the intensity distribution/minimizing the interference effects is especially important in view of axicon/quasi Bessel beam applications in optical coherence tomography [15] and imaging [16,17] where white light sources or spatially incoherent sources were used. A combination of a lens and a fraxicon, similar to the lens–axicon tandem, produces a ring [18], albeit with additional interference rings (Figs. 6 and 7). The ring was obtained at the focal plane of an f ¼ 50 cm lens, and its radius was found to be consistent with the theoretical value [18] R ¼ ðn − 1Þαf ¼ 2:2 cm. The ring width is given by [18]: Δ ¼ 1:05f λ=ω ¼ 54:7 μm, while the experimental values obtained from Figs. 6 and 7 are 52 and 57 μm for the axicon and fraxicon, respectively. We note that the secondary rings have an intensity < 10% of the major peak, and thus the fraxicon–lens (or fraxicon–Fresnel lens) combination can be used for laser machining— especially advantageous where material absorption (e.g., in UV) is a limiting factor. Similarly, the thinness of the fraxicon minimizes dispersion in the material, which may be advantageous in cases such as the generation of Bessel-X waves [19] using an axicon. In conclusion, we have designed, manufactured, and characterized a new element—the fraxicon. Compared to a classical axicon, it is subject to interference effects from the periodic facets and to periodic shadow regions. However, these effects can be mitigated by randomizing the interfacet distance, by using broadband light, or other methods. Consequently, fraxicons may find use in applications requiring a large depth of field, such as imaging, illumination, solar energy collection, and others where minimizing absorption and dispersion of the optical material is important. Moreover, this work proves that the concept of Fresnel lenses can be extended 306
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