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			<titleStmt><title level='a'>Telecentric broadband objective lenses foroptical coherence tomography (OCT) in thecontext of low uncertainty metrology offreeform optical components: from design totesting for wavefront and telecentricity</title></titleStmt>
			<publicationStmt>
				<publisher></publisher>
				<date>03/04/2019</date>
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				<bibl> 
					<idno type="par_id">10161247</idno>
					<idno type="doi">10.1364/OE.27.006184</idno>
					<title level='j'>Optics express</title>
<idno>1094-4087</idno>
<biblScope unit="volume">27</biblScope>
<biblScope unit="issue">5</biblScope>					

					<author>D Xu</author><author>R Chaudhuri</author><author>J Rolland</author>
				</bibl>
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			<abstract><ab><![CDATA[Freeform optical components enable significant advances for optical systems. Amajor challenge for freeform optics is the current lack of metrology methods withmeasurement uncertainty on the order of tens of nanometers or less. Towards addressing thischallenge, optical coherence tomography (OCT) is a viable technique. In the context of lowuncertainty metrology, the design requirements pertaining to the sample arm of an OCTmetrology system are explicitly addressed in this paper. Two telecentric, broadband,diffraction limited, custom objective lens designs are presented with their design strategies.One objective lens was fabricated and experimentally tested for wavefront performance andtelecentricity. This lens demonstrates near diffraction limited performance and a maximumdeviation from telecentricity of 8.7 arcseconds across the full field of view, correlating tomeasurement uncertainty of less than 12 nm in simulation. The telecentricity test methoddeveloped completes the loop with respect to the design requirements and strategies presentedand provides further intuition for telecentric lens designs in general.© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head n="1.">Introduction</head><p>Freeform optical components are gaining traction as they enable advances for optical systems in both performance and packaging <ref type="bibr">[1]</ref><ref type="bibr">[2]</ref><ref type="bibr">[3]</ref><ref type="bibr">[4]</ref>. A major challenge for freeform components is the need for non-contact figure metrology that has sufficiently low measurement uncertainty, is flexible across different surface shapes, and can accommodate for large sag and slope variations. As a rule of thumb, the measurement uncertainty of the metrology instrument should ideally be an order of magnitude lower than the specified tolerance on the optic. As typical figure tolerances may be on the order of &#955;/2 to &#955;/4 <ref type="bibr">[5]</ref>, where &#955; is the wavelength of operation, the uncertainty of the figure metrology should be at most on the order of tens of nanometers for the visible spectrum. Furthermore, it is also desired that the metrology has high dynamic range in terms of surface roughness to not only measure finished components but also to provide iterative feedback during the manufacturing process.</p><p>Towards addressing this challenge, we have been investigating custom Fourier domain optical coherence tomography (OCT) systems for the metrology of freeform optical components <ref type="bibr">[6,</ref><ref type="bibr">7]</ref>. In this technique, the low coherence characteristics of broadband light sources enable optical sectioning through depth. With a sufficiently broad spectral bandwidth and advanced post-processing algorithms, the localization of axial measurements may be pushed to the single digit nanometer level <ref type="bibr">[8]</ref>. In the context of metrology for freeform optical components, the axial measurements correspond directly to the measured freeform sag after accounting for the reference surface. Lateral scanning of the beam across the sample enables three-dimensional volumetric measurements, resulting in point cloud measurements of the freeform under test. By applying telecentric scanning that is the focus of this paper, the OCT metrology system does not require a priori knowledge of the surface under test, thus enabling flexibility across different surface shapes with little to no additional modifications. The range of measurable sag may be up to millimeters and the range of measurable slope may be up to tens of degrees, making this technique especially suitable for small optical components that are one to two inches in diameter. Moreover, OCT is sensitive to both specular and diffuse light signals <ref type="bibr">[9]</ref>, enabling measurements of both rough and smooth optical surfaces along the manufacturing process chain from grinding to polishing.</p><p>To realize an OCT metrology system with the desired characteristics, multiple unique design requirements must be investigated and quantified. System design aspects are seldom discussed in typical OCT literature where the focus is on the application and experimental results <ref type="bibr">[10]</ref><ref type="bibr">[11]</ref><ref type="bibr">[12]</ref>. However, hardware instrumentation design and optimization play a critical role in determining the measurement quality and warrant careful investigation. In this work, the specific design requirements placed on the sample arm of an OCT metrology system and their impact on the measurement uncertainty are explicitly addressed specifically for the case of pre-objective telecentric scanning, where an objective lens focuses the input collimated beam into the sample volume and rotary mirror device(s) enables beam steering via angular control at the objective lens' pupil plane or its optical conjugates. The impact of telecentricity, distortion mapping, image plane flatness, and residual wavefront error on the measurement uncertainty is analyzed.</p><p>Aside from the imaging requirements, signal throughput is another critical design consideration as it directly determines the range of measurable slopes and surface roughness. A typical OCT sample arm configuration is monostatic, i.e. the numerical aperture (NA) of the probing beam forms the solid angle cone that collects the back-reflected or back-scattered light signal. In other words, the typical OCT sample arm acts as both illumination and imaging systems. A challenge in signal collection arises when using OCT to measure optical surfaces when the optics has high slopes as well as when the optical surfaces are polished to be highly specular. One intuitive method to overcome this challenge is to increase the NA. However, increasing the NA typically reduces the depth of focus and consequently the range of measurable sag. Another commonly utilized method is to rotate the objective lens such that the probing beam remains normal to the sample surface <ref type="bibr">[13,</ref><ref type="bibr">14]</ref>. This rotatory degree of freedom is an additional source of uncertainty and in addition it makes it necessary to have a priori knowledge to trace the surface. A bistatic configuration may be envisioned where the illumination and imaging systems are separate and independent of one another. However, this configuration is challenging for interferometry because unavoidable as-built differences result in optical path differences (OPD) that add to measurement error, as will be discussed in Section 2.2. We developed and report here a unique pseudo-bistatic scanning configuration that does not require rotation of the objective lens and retains the necessary depth of focus while maximizing signal throughput, enabling the measurement of arbitrarily smooth optical surfaces over a range of local slopes.</p><p>With respect to the necessary specification requirements for low uncertainty freeform metrology laid out in this work, it was found that commercially available objective lenses do not satisfy these requirements especially in terms of high telecentricity across scan and wide spectral bandwidth over which diffraction limited performance is achieved. Existing off-theshelf OCT objective lenses rarely quantify telecentricity and assume that the user will compensate for it by adjusting the positioning of the rotary mirror device. This assumption is flawed, as will be addressed in detail in Section 2. Highly telecentric lenses exist for the field of machine vision; however, they are typically bi-telecentric and are therefore unsuitable for pre-objective scanning. In this work, two objective lens designs were developed; one was optimized for a large scanning field of view (FOV), while the other was optimized for a large NA and investigates the extent to which the pseudo-bistatic configuration may be applied in practice while balancing manufacturing sensitivity and cost. The design strategy for achieving the necessary requirements is presented and discussed.</p><p>In addition to the design aspects, the large FOV objective lens was toleranced, fabricated, and experimentally validated for both wavefront error and telecentricity. The telecentricity measurement method presented here is a single-shot interferometric method. Currently, the most prevalent method for measuring telecentricity is by using the lens under test to image a resolution target at different axial distances. This conventional method is mostly limited to testing bi-telecentric lenses and is limited in angular resolution and measurement uncertainty, which are determined by the detector pixel size, the travel range of the resolution target, and the quality of this linear travel. The telecentricity measurement method developed here requires no moving elements and is capable of testing lenses that are telecentric in either object or image space as well as bi-telecentric lenses. In addition, the method presented here is capable of not only quantifying telecentricity but also revealing any mis-alignment errors within the lens assembly. The telecentricity experimental results complete the loop with respect to the design strategy described and provide further intuition for telecentric lens designs in general.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.">Impact of telecentricity, distortion mapping, residual wavefront error, and image plane flatness on measurement uncertainty</head><p>For this study in the context of figure metrology, uncertainty is quantified in simulation modelling as the deviation of the as-measured surface from the known nominal prescription. In experiment, this uncertainty includes both accuracy and precision of the measured value with respect to the unknown ground truth. Throughout this work, the image space in optical design terminology refers to the sample space with the freeform under test. It is emphasized that the four aspects analyzed in this section have no direct causality correlation, as will be addressed in detail.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.1.">Impact of telecentricity and distortion mapping</head><p>The telecentricity characteristics and distortion mapping of the objective lens directly determine the resulting beam location mapping across lateral scans, which need to be constrained in design and accounted for in the measurement of the sample optic. Telecentricity is quantified as the absolute value of the maximum chief ray angle at the image plane across the lateral scanning FOV. Distortion mapping is evaluated as the deviation from an ideal f-&#952; mapping of the actual beam position on the image plane or another evaluation plane through focus. The f-&#952; mapping that creates a linear mapping of the scan angle to the beam position is typically desired with scan lenses.</p><p>In experiment, we control the rotary mirror device to perform lateral scanning and obtain volumetric measurement data. The data matrix is therefore organized by the location of the beam as calculated using the mirror angle. Having non-zero distortion translates to having uncertainties in this location mapping in the form of the measurement being "squeezed" or "stretched" artificially, resulting in measurement artifacts not actually present on the surface under test. Even more problematic is when non-zero distortion is combined with nontelecentricity, in which case the distortion mapping varies through focus and results in different mapping errors at different axial planes. Moreover, unless the lens is telecentric, having zero distortion at the best focus image plane does not result in zero distortion through focus. The impact of telecentricity and distortion on the location of the beam on the sample is illustrated schematically in Fig. <ref type="figure">1</ref>.</p><p>In optical design, it is likely under-appreciated that it is generally difficult to have both zero distortion and strict telecentricity at the same time, especially for designs with significant FOVs. As illustrated in Fig. <ref type="figure">1</ref>, between the zero distortion with non-telecentricity case (red) and the non-zero distortion with strict telecentricity case (blue), experimental calibration is more straightforward when strict telecentricity is achieved since the beam centroid location displaces by a constant amount through focus. This aspect determines that for the objective lens design it is best to prioritize telecentricity and evaluate distortion towards the end of the optimization process. Within this design criteria, we next quantify the tolerance on non-telecentricity with respect to the measurement uncertainty. As OCT with telecentric scanning is a point cloud technique that is largely decoupled from the surface under test, it does not matter to the instrument whether the sample surface has rotational invariance. To this end, a simple model with a parabolic surface is shown as follows. A parabola is chosen here to yield an analytic solution, while the results remain meaningful for other surface shapes of similar sag and slope values. For this model, the best focus plane is placed halfway of the total surface sag with zero-distortion at this plane. The chief ray angles of incidence &#952; are assumed to be zero onaxis and linearly increasing toward the edge of the scanning FOV, a scenario not uncommon for a scan lens design.</p><p>Figure <ref type="figure">2</ref>(a) shows half of a one-dimensional slice through the parabolic sample. It can be seen from the shaded triangle in Fig. <ref type="figure">2</ref>(a) that max ' tan( ) 2 ( ')</p><p>where y is the beam location if strictly telecentric, y&#8242; is the actual beam location accounting for deviation from telecentricity, and max z is the maximum surface sag. The functional dependence of y&#8242; on &#952; may be solved using Eq. (1) and Eq. (2) to yield</p><p>The measurement error is evaluated as</p><p>The specifications for the parabola are chosen such that the corresponding maximum sag and slope are representative of the values for freeform optical components that we have surveyed <ref type="bibr">[3,</ref><ref type="bibr">[15]</ref><ref type="bibr">[16]</ref><ref type="bibr">[17]</ref>. For a &#934;30 mm parabola with 2 mm maximum sag and 15&#176; maximum slope (i.e. R = 56.25 mm), the measurement errors with a maximum non-telecentricity of 0.02&#176; are shown in Figs. <ref type="figure">2(b</ref>) and 2(c). As expected, the maximum error appears at the location of highest slope and largest non-telecentricity. For these specific simulation parameters, the errors are well contained within &#177; 30 nm up to approximately 25 mm in diameter, as shown by the green dotted lines in Fig. <ref type="figure">2(c</ref>).</p><p>Best focus Non-telecentric, zero distortion Telecentric, non-zero distortion Telecentric, zero distortion Fig. 2 telece a max with t 2.2. Impact o As OCT is an in the lateral Therefore, an while not the the aberration aberrations w the focus of therefore be d RMS wavefro Another c practice no tw arms into one close to the s beam. This as shown in Sec corollary adva surface, enab masters. The third FOV. In this best fit surfac image plane marks equal between the o the image pla surface is mo that is inhere balancing of latter is referr Petzval curva To further off-the-shelf a With incomin accessible ent Regardless of the real imag resulting in m measured wit 2. 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The educes to g with an in Fig. 3. ner at the ing mode. rbitrarily, measured, at sample o give an</p><p>order of magnitude of this error, at surface I&#8242; and with an operation wavelength of 900 nm, the optical path length of the central ray of the on-axis ray bundle is 208.281 mm while that of the full field off-axis ray bundle is 208.338 mm, resulting in a measurement error artifact of 57 &#956;m at the edge of the field which is approximately three orders of magnitude worse than the required measurement uncertainty as laid out in Section 1. It is worth noting that the setup of Fig. <ref type="figure">3</ref> was optimized for high telecentricity, demonstrating that the measurement error artifact shown is strictly due to a non-flat image plane rather than non-telecentricity with no causality correlation between the two. This means that while one may compensate for telecentricity in practice by adjusting the axial position of the rotary mirror device, it is not consequent that diffraction limited performance will be maintained across a flat image plane. Therefore, in the optical design process for an OCT objective lens, one must optimize for diffraction limited performance across a planar evaluation surface as well as high telecentricity simultaneously.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.">Pseudo-bistatic scanning configuration for enhanced signal collection</head><p>As outlined in Section 1, signal throughput is another critical design consideration especially for finished optical surfaces of high slope that may have RMS surface roughness on the order of single digit nanometers or less. A unique pseudo-bistatic scanning configuration was developed to enable measurement of arbitrarily smooth optical samples without rotating the objective lens nor the sample, while maintaining the necessary depth of focus.</p><p>In this pseudo-bistatic scanning configuration, the objective lens is used with a probing light beam of the same NA as one may use for a typical monostatic configuration, denoted as NA p . This NA p may be determined based on the required depth of focus or diffraction limited spot size. However, the objective lens is to be designed such that it is diffraction limited over a larger collection NA that is responsible for collecting the back-reflected light signal. A schematic layout of this configuration is shown in Fig. <ref type="figure">4</ref>.  where &#952; p is the angle corresponding to NA p and &#945; max is the maximum slope angle one expects the sample surface to have. A corollary design criterion is that the system using this objective lens should also be designed accounting for NA c . In practice, this system level requirement is more readily achieved in optical fiber-based systems compared to free-space ones.</p><p>As can be seen, though the optical components making up the illumination and imaging systems are the same, the sub-sections of those components experienced by the illumination and imaging beams are different, though this difference is constrained by the requirement of diffraction limited performance over NA c . As such, this configuration is referred to as pseudobistatic.</p><p>Under this configuration, the specularly reflected light is captured by the objective lens up to the slope angle &#945; max while maintaining the required depth of focus. As a result, this configuration enables the measurement of arbitrarily smooth samples within its design specifications. By having the objective lens well-corrected over the NA c , it is ensured that the OPD introduced from the optical lens system itself is minimized. A corollary advantage of this configuration is that it removes the need to rotate the objective lens to follow the local normal of the sample surface up to the slope angle &#945; max , thus eliminating errors that may result from the rotary actuation as well as the need of a priori knowledge of the surface. Moreover, as this configuration uses the same probing beam as that for a typical monostatic configuration, it also enables the integration of lenses designed for either configuration under one instrument to extend the measurement dynamic range in terms of sample slope and surface roughness.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.">Telecentric and broadband achromatic objective lens designs</head><p>Aside from the specification targets laid out in Section 2, a broad bandwidth of 360 nm centered at 900 nm was also required for our application to achieve 1 &#956;m axial coherence length with a Gaussian laser source profile. A 2 mm depth of focus in air was also required in accordance with sag ranges found on existing freeform optics, translating to an image space probing beam NA p of 0.0324. Under these specification requirements, we report here two custom objective lens designs that are both highly telecentric and broadband diffraction limited over a flat image plane. One design is for a large FOV monostatic configuration, while the other is for the pseudo-bistatic configuration described in Section 3 with a large NA c .</p><p>With respect to the design strategy for both lenses, it is emphasized that telecentricity is constrained from the beginning of the optimization process. This may be implemented by applying specific constraints to the optimizer merit function and/or by choosing a starting point design that was optimized with some telecentricity target. The specific constraint applied should be one that allows for both positive and negative angular values to enable a stable optimization process. For both design forms, it was found that telecentricity constraints greatly impact the design solutions found and it was in general difficult to recover telecentricity if not designed for without significant trade-off from the other performance specifications.</p><p>With the level of telecentricity requirement indicated in Section 2.1 as guideline, the large FOV objective lens design was pushed for even more stringent telecentricity values nominally to investigate its design limits and to allow for manufacturing margin. It was found that by slowly walking the design form, telecentricity may be pushed to be on the order of 1&#8243; (1 arcsecond = 1/3600 degrees) while maintaining diffraction limited performance over a flat image plane that is 40 mm in diameter. The large NA objective lens functions as a design study to investigate the extent to which the pseudo-bistatic configuration may be applied especially in terms of its scanning FOV. To measure a sample with 15&#176; maximum slope, a mance for the two e FOV objective lens 720 -1080 20, 900, 1080 900 1:1:1</p><p>10 154 0.0324 40 &#177; 7.4 0.05 0.00036 0 33.13 0.16 160 100 e large NA objectiv a significant FO hy lens regime r. This finding nate measuring over the freefo he ability to ca easurement un raint for the l ponds to appro wn in Section 2 de in Table 1 fo ir detailed pres o objective lens e FOV objectiv ricity achieved esigned to hav tween the lens WE achieved is y achieved is rotationally i gs. 6(c) and 6( o objective lens Large NA obj lens 720 -10 720, 900, 1 900 1:1:1 5.5 5 0.55 0.088 &#177; 0.5 0.041 0.068 0 0.037 0.15 12 2.5 ve lens design. OV could e and the indicates g machine orm part. apture the ncertainty. large NA oximately 2.1. or ease of scriptions s systems ve lens is d is 0.8&#8243; &#177; ve a large s and the s 0.0345&#955; 0.046&#176; &#177; invariant, (d) and is The nomin the measurem Table <ref type="table">2</ref>.</p><p>Table 3 Surface # R S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 6. Full field displa NA objective len entricity for (c) the nally achieved ment uncertaint Prescription for Radius (mm) 250.969 -37.211 151.188 -37.216 263.560 156.358 -61.143 189.929 -75.701 155.244 763.000 -89.198 170.067 3. Prescription for Radius (mm) 20.327 8.939 -28.479 -10.193 4.152 -13.494 11.525 -6.622 17.372 5.784 -11.144 2.721 5.892 ay of the nominal ns, both showing large FOV and (d telecentricity v ty using the sim the large FOV ob Thickness (mm) 7.80 5.00 5.66 6.00 9.02 10.80 17.34 9.50 5.00 63.22 11.50 9.50 100.00 r the large NA ob Thickness (mm) 1.00 1.14 0.10 1.00 1.68 0.10 1.39 1.30 0.19 1.60 0.69 1.13 2.50 achieved RMSWE diffraction limite d) the large NA obj values for both mulation mode bjective lens desig Material S-LAH58 S-TIM22 Air S-FSL5 Air S-LAH58 Air S-BSM2 S-TIH4 Air S-LAM2 S-TIH11 Air bjective lens desig Material S-PK57Q1 S-NLAF2 Air S-NKZFS4 CAF2 Air S-NKZFS4 S-SF4 Air O-SFPL51 Air S-NSK11 Air E for (a) the large ed performance. A bjective lens. h designs were el of Section 2 gn. Diameter (m 34.9 34.9 34.9 39.8 39.8 45.9 45.9 49.2 49.2 49.2 70.2 70.2 70.2 gn. Diameter (m 6.2 6.2 6.2 5.8 5.8 5.8 5.8 5.8 5.8 5.6 5.6 4.2 4.2 e FOV and (b) the Achieved nominal e evaluated in r 2.1, the results</p><p>mm) mm) e l relation to of which are shown in Fig. <ref type="figure">7</ref>. The maximum measurement error on the parabolic part due to the nominal residual non-telecentricity from the large FOV objective lens is 0.4 nm while that with the large NA objective lens is 0.9 nm, affording sufficient margins for manufacturing tolerances with respect to telecentricity. </p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.">Fabrication and testing</head><p>The large FOV objective lens was selected for fabrication and testing. This choice was driven by several factors. First, the large FOV design enables lateral scanning over a significant sample area by using rotary mirror device(s) at its accessible entrance pupil plane or its optical conjugates. This optical scanning configuration eliminates the need of mechanical actuation of the sample up to its scanning FOV, which consequently eliminates noise sources associated with the mechanical actuation. Scanning via rotary mirror device(s) is also in general faster than mechanical stages. Secondly, the broad spectral bandwidth necessitates a free-space OCT system due to the current lack of commercially available fiber optic components, for example circulators and couplers/splitters, that can accommodate this spectral range. While the large NA objective lens enables the pseudo-bistatic configuration, under the free-space architecture it quickly becomes resource intensive as all other system sub-assemblies need to accommodate for a beam diameter that is approximately 20x bigger than that with the large FOV objective lens in the monostatic configuration. As such, the large NA objective lens is more suited for fiber-based systems while the large FOV objective lens may be used for both fiber-based and free-space systems. The trade-off with the large FOV objective lens is that it may be challenging to measure very smooth optical surfaces with high slope. However, it is worthwhile to investigate first with this objective lens to benchmark measurement uncertainty. As technology advances, an integrated system is envisioned where the two objective lenses may be mounted together under one instrument to extend the measurement dynamic range in terms of sample surface roughness.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.1.">Tolerancing analysis</head><p>During the design process, manufacturability was controlled for by monitoring the angles of incidence of the rays on each surface of the design and reducing them where necessary. Tolerance sensitivity was also evaluated and controlled during optimization using built-in functions of the optical design software (e.g. SAB and SN2 for CODE V). Tolerancing analysis was performed for polychromatic RMSWE as well as telecentricity across the full FOV. The image plane de-space and the aperture stop de-space were used as the only compensators. The final tolerance values chosen are generally considered to be in the precision category range of tolerances <ref type="bibr">[5]</ref> and are shown in Table <ref type="table">4</ref>.</p><p>It was found that the image plane de-space compensator was effective for the polychromatic RMSWE tolerancing with no effect on the telecentricity tolerancing and vice versa for the aperture stop de-space compensator. The two tolerancing analysis were therefore Table 4. Tolerance table for the large FOV objective lens. Parameter Value Centered tolerances Glass material (n d , &#957; d ) &#177; 0.0005, &#177; 0.5% Radius (larger of two) &#177; 0.1% or 3 fringes (at 546.1 nm) Irregularity (fringes) 0.5 Center thickness for lens elements (mm) &#177; 0.050 Center distance for air spaces &lt; 100 mm (mm) &#177; 0.050 Center distance for air spaces &#8805; 100 mm (mm) &#177; 0.100 Outer diameter (mm) + 0.000/-0.025 Clear aperture 90% Decentered tolerances Wedge, total indicated runout (mm) &#177; 0.010 Tilt (rad) &#177; 0.001 Element decenter (mm) &#177; 0.025 Roll, doublet (mm) &#177; 0.010  <ref type="table">4</ref> for (a) polychromatic RMS and (b) telecentricity. The field points used are shown in the legend that applies to both plots. Larger than 90% yield is achieved for diffraction limited RMSWE and for 0.02&#176; maximum non-telecentricity.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.2.">Assembly and wavefront testing method and results</head><p>The individual lens elements were fabricated and anti-reflection (AR) coated at Kreischer Optics, Ltd. (IL, USA). Since no lens elements were used as compensators, the optomechanical mounting is a monolithic barrel that was designed and fabricated at Bauer Associates, Inc. (MA, USA). The barrel was designed with mounting seats to hold the individual lens elements vertically with gravity. Three radial holes were made around the barrel at each lens element location to allow for the injection of ultraviolet (UV) curable epoxy. The assembled lens system underwent wavefront testing prior to epoxy injection and UV curing.</p><p>The lens assembly and experimental setup for wavefront testing is shown in Fig. <ref type="figure">9(a</ref>). An aluminum spacer tube was precision machined to position a laser fiber output at the image plane of the objective lens to within &#177; 100 &#181;m. The laser (CPS808S, Thorlabs Inc., NJ, USA) outputs at 808 nm, which is within the design wavelength range of the objective lens. The laser is coupled into a multimode fiber, the output tip of which acts as a quasi-point source. The objective lens is pupil matched to within &#177; 1 mm to a commercial camera (Fujinon HF16SA, Fujifilm, Japan), the output of which is monitored via a computer. The camera lens speed is fixed at F/1.6, which results in a magnification ratio of 9.625 with the objective lens speed of F/15.4. At the laser wavelength of 808 nm, the diffraction limited spot diameter on the camera detector is calculated to be 3.15 &#181;m which is smaller than the detector pixel size of 3.45 &#181;m. This configuration means that if the objective lens was made and assembled to</p><p>(0, 0) (0, 14) (0, 20) (0, -14) (0, -20) (-14, 0) (-20, 0) (14, 0) (20, 0) (a) (b)</p><p>achieve diffra field point.</p><p>The result confined to a field and near it can be seen that at on-axi of highest int was audited t mis-match b approximately decrease in in used. As the c likely not AR per air/glass results in fin magnitude of objective lens assembly was action limited ts of the wavef single pixel, in r diffraction lim from Fig. 9(c) s. Figure 9(c) p tensity for each to confirm tha etween the o y 3% vignettin ntensity. It was camera lens is R coated for the interface. The nal transmittan f the observed s has been ma s subsequently 9. (a) Wavefront te g shown in (a) a ing the decrease in ra lens used and n he objective lens h ntricity testing e of the single lens drawing o . 10(a). As can i-parallel to the uggests that if o e able to form fore, deviation by taking th . performance, front testing are ndicating diffr mited performa ) that the intens plots the ensqu h field point, n t it did not vig objective lens ng, which is s deduced that one that was d e near infrared e camera lens nce of 66% to intensity chan anufactured an epoxied and U sting setup for the across FOV, show n light intensity ac not by the objectiv has been manufactu method and e-shot test me of the large FOV n be seen, the e optical axis i one were to se a well-correcte s from a diffra he gradient o then only one e shown in Fig raction limited ance toward th sity at the fulluared energy w normalized to gnette across t and the cam an order of m the most plaus designed for th (NIR) regime, is estimated t o 60% respec nge. The wave nd assembled UV cured. e objective lens ass wing near diffract cross the FOV, wh e lens' opto-mech ured and assemble results ethod develope V objective len central ray of in the image s end in a collim ed focus at the action limited of the aberra e single pixel s g. 9(b). As can performance t he edge of the f -field is approx within a 9x9 gr the on-axis in the field. The mera lens wa magnitude sma sible reason is he visible spect , one may expe to have 4 to 5 ctively, which efront testing r to specificatio sembly. (b) Result tion limited perfo hich was found to hanical housing. Th ed to specifications ed for measur ns design from f each ray bund space with ligh mated wavefron original pupil focus may be ations measure should light up be seen, light toward the cen field. At the sa ximately 50% t rid centered at ntensity. The le maximum 2 m as found to aller than the s due to the cam trum and theref a coating lo 5 lens element matches the results indicate ons. The objec ts of the wavefront formance. (c) Plot o be caused by the he results indicate s. ring telecentric m Fig. 5(a) is re dle across the ht direction fro nt from right to plane, as show e used to quan ed in the Fi p at each is mostly nter of the ame time, to 60% as the pixel ens barrel mm pupil result in observed mera lens fore most oss of 5% ts, which order of e that the ctive lens t t e e g. with flat and an aut for a more q a shear plate i plate is that th lateral shearing directly withou gth of 632.8 n ens, the object values. The tricity over the ens is tested to rameters of th dices. As refra d of the NIR f 0.0251 (occu ected to have velength give ign wavelength operation wave lens is AR coa his observation (Verifire, Zygo &#955;/10 (PV) flat d the positioni between the P the TS and t of the interfer so strong that re on the final ture of the obje modelled in co ed aberrations r ferogram from ion. The objec ations. It was f st method demonst ed here in (a). Th elationship betwee berrations measure forms telecen nabling the us obtain quantita e objective len h a transmissio to-reflecting co qualitative eva inserted in the he average slo g interferomet ut further proce nm was used tive lens was r re-tolerancing central &#934;40 m o be within spe e individual le active indices a design wavel urring at the la a negligible ef direct indicat hs. elength, it was ated for the N n lead to the fin o Corp., PA, U t silver mirror, ing of an iris SI and the obj the iris to blo rogram. This w data could not obtained inter ective lens. ommercial opt resulting from m telecentricity ctive lens was found that the trated with the lar he reverse configur en the planes. Tele ed in (b) config ntricity measur se of existing c ative data, a ns positioned in on sphere and oncave spheric aluation may e collimated sp ope of the wav try and theref essing. for testing and re-evaluated fo at 632.8 nm mm region of in ecifications at enses and their are slowly var lengths) with t ast element m ffect. Therefor tion for the s found that th NIR and these b nal implementa USA) with a F/ as shown in F diaphragm (ID jective lens. A ck strong unw wire placemen t be obtained o rferograms is m tical design s m the alignment alone was fou tilted and dec dominant align rge FOV objective ration is shown in ecentricity may be guration. rement into a configurations Fizeau phase n the typical fa d an auto-refle cal optic). Alter be performed pace of Fig. 1 vefront is auto fore gives the d is outside th or telecentricity shows &gt;90% nterest, as show the He-Ne wa r assembly are rying from 632 the maximum made of S-TIH re, the telecentr expected tele here is significa back-reflection ation shown he /1.5 transmissio Fig. 11(b). The D15, Thorlabs A thin wire (n wanted back-re nt was necessa otherwise. The minimal as the software to is t of the objectiv und to be predo centered as a nment aberrati e n e aberration to realize e-shifting ashion for cting flat rnatively, d with a 10(b). An omatically e average he design y as-built % yield is wn in Fig. avelength, e verified 2.8 nm to m nominal H11), this ricity test centricity ant backns caused ere where on sphere e use of a Inc., NJ, ot shown eflections ary as the e effect of e PSI was olate the ve lens to ominantly whole to ion is 3rd order coma fr mount and the  rom the rotation e coma observe 1. (a) Re-toleranc 90% yield at 0.02&#176; he gradient of e quantified as is step is perfo dimension may d beam space b ntation, we inse widths into th liper was set t orresponding to nal locations w was found tha s from the ima distance, the lo s can be seen v he pixel length d for the telecen 12. (a) Image obta een the objective l y discernable and h dimension across alculated to be 147 50 consecutiv surement. Each pped to the cen o Zernike polyn ms) were remo ly varying, ord n of the lens. A ed in experime cing of the objectiv telecentricity. (b) f the measured s the magnifica rmed after the y be quantified between the ob erted a digital c hat collimated to 30.00 mm. o five indepen within the spac at across the ra ages were all o ower the imp visually from h dimension w ntricity calcula ained with a calip lens and the autoare used to extrac s a range of calipe 7.60 &#177; &#181;m/pix e telecentricity h measurement ntral 40 mm u nomials in the oved as they are ders higher tha As such, the len ent was minimi ve lens at the He-N The experimental d interferogram ation and zoom objective lens by imaging/m bjective lens an caliper (Absolu space, one inst For each calip ndent re-positio e between the ange of widths on the order of pact that this the standard d was calculated t ations. per set to 30.00 m -reflecting mirror. ct the pixel length er widths. Using a xel. y measurement t was processed sing the obtain fringe orderin e purely alignm an Z37 were a ns was mounte ized via rotatio Ne testing wavele l setup for the telec m, the lateral le m ratios taken b has been well measuring an ob and the auto-ref ute Digimatic, tance of which per width chos oning of the ca objective lens tested, the var f 1 pixel or les 1-pixel variat deviation bars to be 147.60 &#177; mm inserted in the The sharp edges h dimension. (b) T all data points, the ts were taken w d as follows. F ned pixel lengt ng. Residual pis ment dependen also removed, ed on a kinema onal adjustmen ength shows larger centricity testing. ength dimensio by the PSI inter aligned to the bject of known flecting flat m Mitutoyo Corp h is shown in F sen, five meas aliper at varyin s and the auto-r riations in the s. In general, t tion has on th in the results &#177; 0.40 &#181;m/pix e collimated space of the caliper are The obtained pixel e length dimension with no phase a First, the obtain th dimension.</p><p>ston, tip, tilt, an nt. As telecentr which is anal atic tip/tilt nts. r on of the rnally are PSI. The n width in mirror. For p., Japan) Fig. 12(a) surements ng lateral reflecting extracted the larger he length shown in el, which e e l n averaging ned phase Next, the nd power ricity is in logous to performing a corresponding measurement in Fig. 13(a) expectation. T within the a measurements maximum me maximum sta the mean. Th uncertainty on than the meas results indica tolerance spec Fig. 1 spheri thin w telece deviat The obtai measurement &#934;30 mm was scanning FOV highest non-t measurement toward the ed 8.7&#8243;) at its measurement Section 1. Th system curren quantified in e 6. Summary In this paper, of low uncert distortion ma systems are r design constr within a rang configuration designs within slope and surf a low-pass fi g fitting coe after taking a where the dom The central co assembly. The s were calcula ean non-telecen andard deviatio he standard dev n the order of sured telecentr ate that the o cifications. 13. (a) Interferog ical aberration as e wire used to block entricity measurem tion of the 50 telec ined telecentr uncertainty u s used to simu V. A one-dim telecentricity error on the p dge of the full steepest slope error was fou his objective l ntly in develo experiment wit y and discus critical design tainty figure m apping, wavefr reported, both raints necessar ge of specifica was develope n one instrume face roughness filter on the fficients were gradient. The minant spheric ma-like fringe e two-dimens ated and are s ntricity was fo on is 2.2&#8243; whic viation of the 0.005&#8243;, which icity and was t objective lens gram of one of t expected from sim k unwanted back r ments with maxim centricity measure ricity test resu sing the simul ulate placing t mensional slice value within parabolic part w l FOV and exp e location to und to be 11.2 ens will be im opment and it th freeform op sion n requirements metrology for f ront error, and of which are ry to optimize ations. To max ed. This config ent to extend t s. data. The re e then used interferogram cal aberration es may be due sional mean a shown in Figs ound to be 8.7&#8243; ch is approxim pixel length d is approximate therefore deem has been fab the telecentricity mulation in optical reflections may als mum of 8.7&#8243; and ments with maxim ults were eva lation model p the &#934;30 mm p through the t the &#934;30 mm was found to b periences the l simulate a nm, meeting t mplemented in ts measuremen tic samples. are detailed fo freeform optica d image plane e designed wit the OCT me ximize signal guration also en the measureme emaining Zer to obtain th of one of the m is clearly visib to slight tip/ti and standard s. 13(c) and 1 &#8243; with RMS of mately four tim dimension was ely three order med to have a n bricated and a measurements, sh design software. T so be seen. (b) Th d RMS of 0.8&#8243;. mum of 2.1&#8243; and R aluated in rel presented in S parabolic samp two-dimension m region was be 1.2 nm. If th largest non-tel worst-case sc the metrology n a custom OC nt uncertainty or the OCT sam al components flatness. Two th the specific etrology system throughput, a nables the inte ent dynamic ra rnike terms a he final tele measurements ble, agreeing w ilt of the lens deviation of 13(d) respectiv f the mean of mes smaller tha s found to intr rs of magnitud negligible effe assembled we howing dominant The shadow of the he mean of the 50 (c) The standard RMS of 0.2&#8243;. lation to the Section 2.1. Th ple at the cent nal data conta used. The m he parabola w lecentricity ov cenario, the m requirement la CT freeform m y contributions mple arm in th s, namely telec o custom objec cations and ap m for measurin unique pseud egration of the ange in terms o and their centricity is shown well with elements f the 50 vely. The 0.8&#8243;. The an that of roduce an de smaller ect. These ell within t e 0 d freeform he central ter of the aining the maximum as placed verall (i.e. maximum aid out in metrology s will be he context centricity, ctive lens ppropriate ng optics do-bistatic two lens of sample</p><p>One of the two lens designs reported was toleranced, fabricated, and tested for both wavefront performance and telecentricity. The single-shot telecentricity test method reported here is versatile for a range of telecentric lens configurations. For example, one may use a transmission flat and an auto-reflecting flat mirror to test a bi-telecentric lens. For a telecentric objective lens without an accessible entrance/exit pupil, for example the large NA objective lens presented here, additional steps need to be implemented to align to the internal pupil plane. Compared to the existing method of imaging a resolution target through axial distances, this method has finer angular resolution and is faster and more robust as it eliminates the large linear travel. Another interesting characteristic of this test method is that by essentially exchanging the chief ray with the marginal ray, telecentricity may be tested independently of the imaging or wavefront performance. For this method, it is crucial to know the length dimension of the pixels. A way in which the uncertainty of the telecentricity measurement may be improved is by precision machining fiducial markers of a known width apart on a component surface in the collimated space, for example the auto-reflecting flat mirror in the implementation shown here.</p><p>During the design process of the two objective lenses, it was found that there is a significant trade-off between achieving high telecentricity and diffraction limited performance over a flat image plane. To first order, telecentricity may appear straightforward to achieve by placing the entrance pupil (or the rotary mirror device in practice) at the front focal plane of the objective lens. However, it becomes apparent that aberrations will result in deviations from this first order design when one recognizes that telecentricity is, by definition, imaging the pupil plane to infinity. As with any other imaging configurations, corresponding aberrations need to be optimized for during the design process. This aspect may be further illustrated by the telecentricity test method present there. If we apply this test method to the doublet configuration shown in Fig. <ref type="figure">3</ref>, since it is in general challenging for a single doublet to form a diffraction limited focus for a collimated beam of broad bandwidth and large diameter, it becomes intuitive that in reverse it is challenging to achieve high telecentricity with a doublet without sacrificing wavefront performance on a flat image plane over a large scanning FOV. Conversely, a lens that is designed to form a diffraction limited focus for a large diameter collimated beam may be a suitable starting point for a telecentric objective lens design. The balancing between achieving high telecentricity and diffraction limited performance on a flat image plane ultimately leads to a more complex lens design compared to a non-telecentric counterpart.</p></div><note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_0"><p>Vol. 27, No. 5 | 4 Mar 2019 | OPTICS EXPRESS 6185</p></note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_1"><p>Vol. 27, No. 5 | 4 Mar 2019 | OPTICS EXPRESS 6197</p></note>
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