Measurement of focusing properties for high numerical aperture optics using an automated submicron beamprofiler
aa r X i v : . [ phy s i c s . op ti c s ] S e p Measurement of focusing properties forhigh numerical aperture optics using anautomated submicron beamprofiler
J. J. Chapman, B. G. Norton, E. W. Streed and D. Kielpinski
Centre for Quantum Dynamics, Griffith University, Queensland, Brisbane 4111 [email protected]
Abstract:
The focusing properties of three aspheric lenses with numericalaperture (NA) between 0.53 and 0.68 were directly measured using aninterferometrically referenced scanning knife-edge beam profiler withsub-micron resolution. The results obtained for two of the three lensestested were in agreement with paraxial gaussian beam theory. It was alsofound that the highest NA aspheric lens which was designed for 830nmwas not diffraction limited at 633nm. This process was automated usingmotorized translation stages and provides a direct method for testing thedesign specifications of high numerical aperture optics. © 2018 Optical Society of America
OCIS codes: (120.4630) Optical inspection, (120.4800) Optical standards and testing,(110.3000) Image quality assessment, (220.4840) Testing
References and links
1. S. M. Mansfield, W. R. Studenmund, G. S. Kino, and K. Osatot, “High-numerical-aperture lens system for opticalstorage,” Opt. Lett. Optical shop testing, ” (Wiley, New York, 1992).11. Yasuzi Suzaki and Atsushi Tachibana ”Measurement of the m m sized radius of Gaussian laser beam using thescanning knife-edge,” Appl. Opt. Lasers, ” (University Science Books, Sausalito, 1986). . Introduction
There are a number of processes which rely on tightly focusing light for which the shape andsize of the spot must be known to achieve the desired outcome. For example, optical memoryis now a common method for data storage. As advances in other aspects of these systems aremade (such as increased resolution of optical pickup [1]) the optics must focus higher frequencylaser light tightly and reliably. Optical trapping by tightly focused lasers has been widely usedfor the manipulation of sub-micron sized particles. The force in these traps is proportional tothe gradient of intensity, and is therefore controlled by the quality and spot size of the focusinglens [2,3]. Improving the signal-to-noise ratio in fluorescence spectroscopy of single moleculesis achieved by reducing the detection volume determined by the spot size which is directlyrelated to the numerical aperture of the focusing objective. To achieve maximum collectionefficiency it is therefore very important that the spot size and quality of the lens is as expected[4,5]. Advanced optical imaging methods such as stimulated emission depletion microscopy [6]or 4 p microscopy [7] need lenses with the highest numerical aperture possible to achieve thehighest imaging resolution and fluorescence collection efficiency. All these applications requireprecise knowledge of the lens’s focal spot to correctly predict and evaluate experimental results[8,9]. It is therefore necessary to first be able to accurately characterize the optic’s focusingability.High numerical aperture (NA) optics are currently characterized using three common testmethods [10]; 3d profilometers, null tests and the Hartmann test . These methods measuresurface geometry of optics and use that information to reconstruct the element’s focusing prop-erties. It is more reliable to characterize the optic’s performance at the focus directly as thisis the experimentally most relevant position. While there are many beam profiling units com-mercially available for this purpose, none have adequate resolution for measuring submicronspots. The knife-edge scanning technique is a well known process which has the ability to per-form submicron waist measurements. This process finds the beam waist by scanning a razorthrough the beam and measuring the corresponding change in transmitted power. This has beenpreviously been used to characterize submicron spots [11-13], but these experiments lacked theautomation required for efficient and rapid testing. We used motorized translation stages to au-tomate the test process, with accurate velocity calibration provided by an interferometer. Inputbeam size and spot size were measured for a number of aspheric lenses in order to demonstratethe apparatus.
2. Apparatus
In order to measure the optics’ focusing ability and investigate the spot size directly, an auto-mated beam profiler with submicron resolution was constructed. The apparatus is shown in Fig.1. A razor is attached to one side of the translation stage and a mirror is attached to the oppo-site side. In this way the stage acts simultaneously as the scanning element and the reflectorfor one of the interferometer arms providing an accurate velocity calibration in the directionperpendicular (x-axis Fig. 1) to the beam. 632.8nm light from a helium-neon laser was usedin the interferometer and for testing the lens. Two precision motorized translation stages withresolution of about 50nm were used to automate the beam profiling process. The power in thebeam is measured real-time while the razor is cutting the beam through the x-axis in Fig. 1 , andthe interferometer calibrates the razor’s velocity. By observing the interference fringes it wasdiscovered that the motors do not move at their nominal velocity, implying the interferometeris critical to obtain an accurate result. In contrast, errors in stage movement parallel to the beam(the z-axis in Fig. 1) were not found to limit the measurements.The laser light was delivered to two single mode fibers to provide increased flexibility and re-liability of the system. One fiber output provides light to the interferometer. The other output is
Fig. 1. Beam profiling apparatus-translation stage scans the razor through the beam whileacting as one of the interferometer arms providing accurate distance calibration for thewaist measurement of the focused beam collimated, sent through an expansion telescope of variable magnification and coupled into thetest lens. The lens position and the beam’s angle of incidence is controlled by an xyz translationstage and mirror. Proper alignment of the beam through the lens is achieved by measuring thedependence of the beam waist on each of the four alignment variables - horizontal and verti-cal angle of incidence, and horizontal and vertical position of lens, then setting each variable tominimize the observed waist size. This procedure is iterated until convergence. A gimbal mountwas used for the mirror immediately before the test lens to ensure the horizontal and verticalchanges of angle are decoupled. Once the lens was properly aligned the knife-edge scanningmethod was used to obtain waist measurements along the length of the focused beam. To en-sure that the roughness of the blade did not affect the measured spot sizes we obtained an SEMimage of the razor edge. The error in the waist measurement can be assumed insignificant forspatial variations outside the scale of d ≥ d x ≥
10d where d is the 1/ e diameter of the beamand d x is the size of the variation. The RMS roughness over this range was 0.035 m m, negligiblecompared to other errors.
3. Results and Discussion
Paraxial Gaussian theory predicts that a beam of 1 / e radius w incident on a lens with focallength f will focus to a spot size w under the relation given by Eq. 1 [14], where the spot size w is the 1 / e radius of the beam at the focus. w w ≈ f lp (1)This equation was used to calculate the theoretical spot sizes for each combination of lensand input beam size. The raw data obtained from the apparatus consists of an error functionrepresenting the power in the beam, and sinusoidal interference fringes from the interferome-ter as shown in Fig. 2. The interference fringes are fit with a sinusoidal function of the form Asin ( a + a t + a t + a t ) + B where A , B , a , a , and a are fit coefficients and t is time.It was found that adding higher order terms in terms did not significantly improve the fit. Thechange in power of the beam as the razor was scanned across was measured over time. The timeaxis was then converted to a calibrated distance scale for every scan. The x-axis distance foreach set of knife-edge data was re-fit with its calibration data allowing the waist of the beam tobe known.Approximately 20 of these scans are recorded at intervals along the length of the beam cen- Fig. 2. Typical interferometer (upper panel) and knife-edge (lower panel) data for a singleknife-edge cut. Dots: Data, Solid line: fit to sinusoid (upper panel) and Gaussian powerdistribution (lower panel) tered around the focal point. The waist measurements from each of these scans was tabulatedand fit with Eq. 2. This equation gives the spot size and Rayleigh range of the beam. w ( z ) = w q + [ z / z R ] (2)The Rayleigh range of an ideal gaussian beam with the same waist w is calculated using theequation Eq. 3. z R = p w l (3)The ratio of the ideal and measured Rayleigh ranges z idealR / z measR gives the M value for thatparticular beam expansion.We tested three aspheric lenses from Kodak and Lightpath, their properties are summarized intable 1. Waist measurements for the collimated output from the single-mode fiber were recorded Table 1. Design specifications of aspheric lenses
Lens NA Focal length Design wavelength Clear aperture(mm) (nm) (mm)Kodak A390 0.53 4.6 655 4.89LightPath 350330 0.68 3.1 830 5LightPath 352671 0.6 4.02 408 4.8
Table 1. Properties of aspheric lenses used for testing. using a commercial CCD beam profiler over 1.2m. The spot size and M of the beam were de-termined to be 350(30)um and 1.02(1) respectively, so the input beam is well approximated by apure Gaussian beam. The beam expansion telescopes introduced a maximum beam divergenceof 90 m rad. This should not affect the M but introduces a maximum error of 0.1 m m to themeasured spot size. The telescope optics were large enough to ensure a negligible contributionto diffraction of the beam at the largest beam expansion.The intensity ripples in the near field caused by diffraction are approx 1% of the amplitudeat the condition 2 a = . w where a is the radius of the clear aperture and w is the waist ofthe input beam [14]. For larger input beam sizes diffraction effects become significant and havethe effect of increasing the spot size, divergence and M of the beam. To facilitate comparisonsof the different lenses, we define the fill-factor as the ratio of the input beam waist and clear Fig. 3. M and spot dependence on fill-factor for Kodak A390 lens. Dots: Data, Red solidline: Ideal gaussian and Blue solid line: measured beam. M ^ Fill factor S po t s i z e ( u m ) Fill Factor
A390
Fill Factor
Fill Factor
Fig. 4. Spot size and M as a function of fill-factor for each lens. The condition of 1%diffraction effects is represented by the dotted line. Dots: Data, Solid line: Theoretical spotsize (lower panel). aperture, so that the 1% amplitude criterion corresponds to a fill-factor of 0.22 in all cases. Theerror in the fill-factors in Fig. 3 arises from the uncertainty in the input beam waist. The KodakA390 and LightPath 352671 lenses both showed an increase in the M at this condition. Theresults for the Kodak A390 lens are shown in Fig. 3. The figure shows the divergence for theactual beam in blue and the divergence for an ideal gaussian beam in red.The LightPath 350330 however showed an increase in M at 0.14(1) fill-factor. Only fourdata points were taken for this lens since its performance was not diffraction limited as demon-strated by the rapid increase in M . The LightPath 350330 aspheric lens is the highest numericalaperture lens readily available commercially, and also has the largest clear aperture out of thethree lenses tested. It is designed to operate at 830nm and was tested at 632.8nm, which couldexplain the deviation from diffraction limited performance.These results are summarized in Fig. 4, which demonstrate the dependence of spot size and M on input beam size. The error in the fill-factor in Fig. 4 is also due to the uncertainty ininput beam waist, as in Fig. 3.
4. Conclusion
An automated method for testing the focusing properties of high numerical aperture optics withsubmicron resolution was demonstrated. Test results for aspheric lenses of NA up to 0.68 werein agreement with the limits of paraxial gaussian beam theory with the inclusion of clippingeffects for input beam sizes that overfilled the lens aperture. It was further determined that onef the aspheric lenses was not diffraction limited, possibly because the lens was not tested at itsdesign wavelength.
5. Acknowledgements5. Acknowledgements