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Shack-Hartmann wave-front sensing has been successfully applied to many fields of optical testing including the human eye itself. We propose wave-front measurement for testing protective eye wear for production control and investigation of aberrations. Refractive power data is derived from the wave-front data and compared to a subjective measurement technique based on a focimeter. Additional image quality classification was performed with a multivariate model using objective parameters to resample a subjectively determined visual quality. Wave-front measurement advances optical testing of protective eye wear and may be used for objective quality control.
©2012 Optical Society of America
1. Introduction
Personal eye protection is an important issue in many fields, for example construction and metal work as well as laboratory work and science. Modern eye protection devices fulfill high protection standards defined by the International standard ISO 4849 as well as the newer American standard ANSI Z87.1 and the European standard EN 166 [1–3]. The materials used (mostly polycarbonates) have to resist mechanical and possible chemical impacts, such as might occur in clinical practice and chemical or biotechnical labs [4]. In addition to the high protective demands, the optical tolerances for eye protection of ‘optical class 1’ are smaller ( ± 0.06 D spherical and 0.06 astigmatic power) than for ophthalmic lenses ( ± 0.12 D for lenses < 9 D [5]), which is equal to the definition of ‘optical class 2’ according to the International and European standards [1–3]. The ISO standard defines a third optical class with a tolerance limit of + 0.12/-0.25 D spherical and 0.25 astigmatic power [1]. The newer ANSI standard only defines a single optical class with limits of 0.06 D [2]. Additional desired product properties (protection, minimum thickness, curvature, design) have to be considered for design of the lenses. Production processes (injection molding) and coating may cause mechanical stress within the polycarbonate lenses causing degradation of optical quality. Finally the assembly and use of some eye protectors may set the otherwise plano lens under stress which often causes astigmatism due to deformation. On the other hand sufficient optical quality is required to prevent eye fatigue, headaches and finally loss of concentration or nausea which may lead to refusal of the eye protection [6]. Therefore basic optical testing is mandatory according to current standards [2,7,8].
In this study we focused on advanced optical testing regarding refractive data of the eye protector lens. Material characterization such as scatter measurement was not the scope of the current study. According to the current regulations, the refractive power of the eye protector has to be within ± 0.06 D spherical equivalent power and within 0.06 D absolute astigmatic power to be classified as `optical class 1` or ‘grade 1’ [1–3]. The required accuracy and test zone for this measurement are out of the measurement range of common focimeters, however, newer devices are verging to this accuracy. The standards suggest a test setup for testing of long focal lengths which is based on afocal imaging and visual inspection of a cross-bar test target (Fig. 1 , ANSI specifies a similar method) [2,7,8]. However, using this method, testing is limited to a pass/fail-test for refractive power and image quality. Detailed information about the aberrations is not available and higher order aberrations cannot be investigated sufficiently.
Fig. 1 The measurement principle of the optical bench setup follows the principle of a focimeter. The observer focuses on the rotatable target to determine the power of defocus (sphere) and power and axis of astigmatism. Left: the standardized test target used for power measurement and image quality classification [7,8]. The image on the right shows an example of a blurred test target with a subjective image quality (SI) grade of > 3.
We believe that it is important to measure the entire aberrations of protective eye wear in use to determine concise information on the imaging quality and potential influence factors for lens production. This includes the refractive data (sphere and astigmatism) but also higher order errors like spherical aberration, trefoil or coma. In the advent of modern curved lenses, also the change in aberrations with view port (aperture around an arbitrary axis of vision) through the lens, line of sight, pupillary distance (PD) and head width should be addressed. The concern on various head widths became important since modern flexible ear pieces are designed to apply a limited amount of force on the back head to ensure a good fit. Therefore, the lens itself is slightly bent which induces internal stress causing an increase in aberrations (depending on mechanical and optical design approximately + 0.02 D of astigmatism between 150 mm and 180 mm head width).
Wave-front sensing has been applied for characterizing a number of different optical systems, such as ophthalmic photographic lenses, intraocular lenses as well as the human eye itself. The robustness of the Shack-Hartmann-test against vibration and the low requirements for coherence of light make it a useful tool for fast and accurate industrial optical testing compared to interferometers. Several commercial optical test devices such as focimeters use the Hartmann or Shack-Hartmann technique. In this paper we propose a test setup for detailed optical testing of eye-protectors in terms of wave-front sensing with a Shack-Hartmann wave-front sensor. The purpose was to improve the accuracy of refractive power measurement, to improve the assessment of image quality and to investigate the aberrations which cause image blur in eye protectors. This will enable the definition of better classifiers for pass or fail in quality control and allow investigation of the sources of error within the production process.
2. Material and methods
Optical bench setup
The optical bench setup which was used for subjective/visual inspection of the eye protector lens is shown in Fig. 1. A telescope objective is used for observation of an illuminated test target mounted at a distance of 4.6 m from the eye protector according to ISO 4854 and EN 167 [7,8] (the ANSI test is similar using a distance of 10.67 m [2]). The telescope is equipped with a turning knob which allows spherical power adjustment with a graduation of the scale in steps of 0.01 D. This optical bench setup works like an oversized manual focimeter. The eye protector was clamped into a holder directly in front of the telescope objective, centering the telescope aperture to one side of the eye protector. Left and right sides (corresponding to the left and right eye) were tested sequentially. The field of view was limited by a circular aperture stop of 20 mm in diameter which is mounted at the front lens of the telescope (other aperture diameters could also be used).
A trained person observed the illuminated test target without using any filter and adjusted the telescopes tube length until sharp imaging on one principal axis was reached. The spherical power for this meridian was recorded as power D1. Then the telescope was refocused for a sharp image in the orthogonal meridian, which is at power D2. Astigmatic angles outside of 0° could be adjusted by rotating the target around the optical axis. Spherical equivalent power (SEQ) and astigmatic power (AST) were then defined as SEQ = (D1 + D2)/2 and AST = |D1-D2| according to [3] and the values were quantized to steps of 0.01 D. A preliminary internal study revealed that the trained person performed with a repeatability of ± 0.01 D or slightly better.
Wave-front setup
We applied a single-pass Shack-Hartmann test for measuring the wave-front aberration of eye-protector lenses. The optical setup uses a red single mode fiber coupled diode laser (λ = 638 nm, NA = 0.13) as light source. The laser beam is expanded and collimated to a diameter of 20 mm (1/e2) which refers to the mandatory test diameter according to ISO 4854 (15 – 20 mm) EN 167 (elliptical: 20 x 22 mm) [7,8]. The plane wave front from the collimation optics propagates through the eye protector lens under test. The aberrated wave-front then propagates to the measurement plane which is imaged onto the Shack-Hartmann-sensor by an imaging telescope (Fig. 2 ) with a magnification of 3.4:1 to ensure that the entire test area can be recorded using a standard 2/3” CCD camera.
Fig. 2 Schematic layout of the measurement setup used for characterizing the eye protector lenses and mounted goggles. The plane wave-front passes the eye protector lens and is imaged on the Shack-Hartmann sensor (SHS) by a telescope (the solid and dashed green lines show the conjugated planes).
The sensor head (SHSLab HR, Optocraft GmbH, Erlangen, Germany) has a refractive micro lens array (69 x 51, 130 µm circular aperture). Spot-image evaluation, wave-front reconstruction and Zernike analysis were performed with SHSWorks 10 (Optocraft GmbH, Erlangen, Germany). The size and focal length of the micro lenses and the CCD resolution determine the angular resolution and the theoretical dynamic range of the sensor.
According to the equations of Awwal and Olivier, the dynamic range of our sensor system is > 0.71 D with a sensitivity of better than 0.002 D when assuming a sub pixel detection of 1/20 pixel width [9].
After self-referencing and subtraction of the internal aberrations, the residual wave-front error was less than λ/5. Refractive power calibration of our system was accomplished using a set of calibrated lenses with powers of −0.27 D, −0.06 D, 0.00 D, + 0.07 D and + 0.25 D and applying a 4th order calibration polynomial. We developed custom software in C#.NET which allows a batch mode for testing in different the eye protector in oblique axes of vision.
Head model
The eye protectors under test were mounted on a simplified head model which mimics nose and a variable head width (Fig. 3 ). The head model itself is mounted on three motorized stages for lateral translation (linear stage), rotation (rotational stage) and inclination (goniometer stage) to allow measurement at different view ports. The dimensions of the head model were adopted from the head form dimensions used for mechanical testing with a head width of 155 mm. The head model additionally allows mimicking different wearing positions by adjustable nose bar and different head widths by adjustable ear-bars.
Fig. 3 a) Simplified head model with variable nose bar (green) and head width (red). The standard head width was set to 155 mm. b) Example of an eye protector in the wave-front device.
Samples
A representative sample of 50 spectacle-like eye protectors of each of two geometrically similar eye protection devices was taken (Table 1 ). Both eye protector models are based on the same optical design, but use different frame types and are produced in different cavities. All eye protectors were produced by injection molding within the standardized production process. None of the lenses had an additional coating.
Table 1. Descriptive data of the eye protectors. Refractive power data and subjective image quality (SI) were measured on the optical bench and is provided in 10−2 D units as spherical equivalent power (SEQ) and absolute astigmatism (AST). SI is given in classes (1 = excellent, 2 = good, 3 = slight errors, 4 = unacceptable).
The entire sample set was classified as ‘optical class 1' according to the industry standard in terms of refractive power less than ± 0.06 D. The eye protectors were tested on the optical bench by a trained person using the target shown in Fig. 1. Each side (right/left) of the lenses was graded into 4 clusters of image quality (SI, 1 = excellent, 2 = good, 3 = slight errors, 4 = unacceptable) and the refractive power data was recorded. All lenses were tested with the same pupillary distance (PD = 64 mm).
The vertical position was adjusted for each eye protector model to provide an in-use-position which we defined as vision through the central part of the lens. Both sides (left and right) of the lenses were measured sequentially without removing the eye protector from the head. Wave-front data, Zernike coefficients and the refractive power data (spherical equivalent and absolute astigmatic power) were recorded. The results were taken for an intra- and inter-model comparison between eye protector models 1 and 2.
Statistical analysis
A total of 200 measurements (wave-front and optical bench) of 100 eye protectors were compared in terms of sphere, cylinder and image quality by means of ‘optical class’ determined by visual inspection. Twenty-five samples of each model were produced in one mold referred to as mold 16 for model 1 and mold 1 for model 2, another 25 in an adjacent mold referred to as mold 26 and 2, respectively. Right and left sides (corresponding to the right and and left eye) of the eye protector lenses were treated as connected cases, as they have to be tested separately but either one of them can result in rejection of an eye protector lens.
We compared the spherical equivalent (SEQ) and astigmatic power (AST) from optical bench and wave-front test as well as the difference between left and right side subjective image quality (SI). A non-parametric U-test (Wilcoxon) was used to test for significant intra-item differences of refractive power data between left and right sides. In a second step we compared the inter-item differences using a parametric t-test. All statistical calculations were performed for the refractive power data from the optical bench and wave-front test as well as for SI. In addition, we applied a multivariate linear regression model on the complete sample set (all sample lenses) to check whether the subjective image quality classification (SI) could be predicted from wave-front parameters. All statistical evaluations were performed with the statistics software IBM SPSS version 19. The results were analyzed by means of descriptive statistics and a multivariate linear regression model was applied. The predictability was checked by ANOVA.
3. Results
Wave-front analysis showed strong correlations (Spearman) between distinct Zernike coefficients and SI which give an impression of the type of aberrations that typically deteriorate image quality in those lenses. For the tested samples we found that spherical aberration (Z8, ρ = 0.906, P < 0.001) and 2nd order astigmatism 0° (Z11, ρ = 0.906, P < 0.001) were most prominent, followed by astigmatism 0° (Z4, ρ = 0.631, P < 0.001), trefoil 0° (Z9, ρ = 0.529, P < 0.001) and 2nd order coma (Z14, ρ = 0.583, P < 0.001). However, the 45° components of these aberrations showed only weak correlation with SI.
Figure 4 shows the magnitude of the higher order aberrations in the three image quality groups. Primary coma and trefoil seemed to have an effect on image quality degradation, followed by secondary astigmatism and primary spherical aberration.
Fig. 4 Absolute magnitude of aberration in microns among the image quality (SI) groups. Error bars specify the 95% confidence limits for each aberration type.
As the eye protectors are based on a single sphere, meaning the lens is a single curved surface instead of two curved surfaces for both eyes, we hypothesized similarity between left and right side SEQ. The Wilcoxon test resulted in a highly significant difference for SEQ measured on the optical bench but no significant difference for the wave-front measurement (P = 0.001/0.367 for model I and P = 0.011/0.377 for model II). The measurement of astigmatic power showed a highly significant difference for both measurement techniques for model II (P = 0.001/0.003) but no significant difference for model I (P = 0.907/0.308). SI classification of left and right sides was significantly different in model II (P < 0.001) and there was no difference for model I (P = 1.0). This was an expected result as only the right sides of model II had an SI of 3 and left sides an SI of 2 whereas model I had an SI of 1 throughout all sample lenses.
Spearman’s correlation coefficient was calculated to check the correlation between the measurements. The correlation coefficients of SE (ρ = 0.711; P < 0.001) and AST (ρ = 0.787; P < 0.001) were highly significant. We also found significant correlation between SI and SE for the optical bench (ρ = 0.414; P < 0.001) and the wave-front test (ρ = 0.207; P < 0.003) as well as for SI and AST (ρ = 0.440; P < 0.001 and ρ = 0.494; P < 0.001). Figure 5 and Fig. 6 also reveal, that the differences between the two measurement devices are greater for model II than for model I taking into account that only model II had samples with SI > 2. This indicates that aberrations deteriorate the measurement of sphere and astigmatism on the optical bench, whereas the wave-front analysis uses only pure defocus and astigmatism polynomials for calculating spherical and astigmatic power.
Fig. 5 Comparison of spherical equivalent measurement between optical bench and wave-front sensor. The scatterplot (a) shows the perfect angle bisector (solid line) along with the range of measurement inaccuracy of ± 0.01 D (dashed lines). The histogram (b) shows the relative frequencies of the differences between the two measurement systems along with a normal distribution curve.
Fig. 6 Comparison of absolute astigmatism measurement between optical bench and wave-front sensor. The scatterplot (a) shows the perfect angle bisector (solid line) along with the range of measurement inaccuracy of ± 0.01 D (dashed lines). The histogram (b) shows the relative frequencies of the differences between the two measurement systems along with a normal distribution curve.
Objective classifier
The parameters derived from the wave-front data were used to create a model for an objective image quality classifier (OI) similar to the subjective image quality classifier (SI). We included Zernike coefficients Z3 to Z15 (according to DIN-ISO 10110-5: defocus to secondary spherical aberration) as well as the Strehl ratio (SR) into a linear regression model (Eq. (1) and Fig. 7 ). The coefficient of determination (R2) revealed an excellent predictability of SI by OI (R2 = 0.998).
Fig. 7 Correlation of the objective classifier (OI) with the subjective classifier (SI) including the limits of the 95% interval of confidence.
4. Discussion
In eye protection the aim is to protect the eye from possible mechanical, chemical or radiative hazards (e.g. splints, acids or laser radiation) without introducing additional hazardous issues such as an unwanted refractive effect. Therefore, optical testing of eye protection is an important issue which demands the same amount of attention than the protective effect. Current regulations define strict tolerances for residual refractive power of eye protectors ( ± 0.06 D spherical equivalent and 0.06 D astigmatism for ‘optical class 1’ or ± 0.12 D for ‘optical class 2’) [1–3]. The standardized assessment of the image performance is limited to a visual inspection of a bar target (Fig. 1) which is suitable for evaluation of the spherical and astigmatic power and a subjective image quality grading. Higher order aberrations, however, can only be identified as image blur.
The International and European standards also propose a second even more precise test method for refractive power and image quality testing which is based on a ray-tracing method (Annex A in [7,8]) to create a prismatic deviation map which allows detailed investigation of aberrations. The method uses a collimated laser beam (λ = 600 nm ± 70 nm) with a nominal beam diameter of 5 mm. The eye protector is mounted on a actuator which is able to move the eye protector laterally to the beam in a spiral way. A position sensitive photodiode is used to detect the beam deflection for each position in a distance of 0.5 m to 2.5 m to the eye protector [7,8]. This method allows an accuracy of 10−5 D according to ISO 4854 [7] and allows local analysis of aberrations. However, this type of measurement setup does not allow deep investigation on the type of aberrations and the cause of aberrations in production of eye protectors.
The functionality of such type of a measurement setup could be completely replaced by a wave-front sensor which allows investigation of the Zernike aberrations, refractive power values and calculation of the point spread function and optical transfer function via software. Refractive power and image quality testing is only required for straight vision, there is no requirement for oblique axis measurement which may be important in case of eye protectors with steep base curves. However, the relatively large test area of 20 mm in diameter accounts for different pupil distances, spectacle inclinations as well as for portion of oblique axis vision. To our knowledge, this mainly accounts for perifoveal vision, but not for eye movements (e.g. while reading).
We presented a test setup based on wave-front sensing with a Shack-Hartmann wave-front sensor. This test is very precise when testing deviations from a plane wave as required in the testing of protective eye wear. Shack-Hartmann wave-front sensing is robust and allows high measurement speeds compared to high precision interferometric methods which make it ideal for industrial testing. Therefore, this technique has also been included into commercial focimeters such as the Nidek LM-1800PD [10]. We added the functionality of measuring in oblique axis to mimic various gaze angles through the eye protector, whereas most devices measure in straight view situation. The major disadvantage may be the spatial sampling which is mainly limited by the size and number of micro lenses, the size of the CCD and the magnification of the imaging telescope. The spatial sampling should be chosen carefully so that errors with small spatial extent are still detectable. We used a spatial sampling of approximately 44 sampling points within the 20 mm test diameter which refers to a sampling density of 2.3 mm−1 in the measurement plane. The total number of measurement points within the measured area was 1895 spots. Current commercial Hartmann-based focimeters, such as the Nidek LM-1800PD use a measurement beam with 108 subapertures/spots for measurement which is scanned over the lens aperture which provides a similar spatial resolution but limits the measurement speed [10].
Our system had an estimated dynamic range of better than 0.71 D and a sensitivity of better than 0.002 D [9]. In fact the dynamic range of the employed Shack-Hartmann system is approximately 10 times higher due to the enhanced spot-location-algorithm [11]. However, additional calibration for this measurement range is required. The dynamic range of our standardized ‘optical bench’ setup is about 0.5 D with a scale-reading precision of 0.01 D and an estimated sensitivity of 0.005 D.
We found that the primary aberrations causing image quality degradation were primary coma and trefoil followed by spherical aberration and secondary astigmatism as well as secondary coma. Fernández-Sánchez found that approximately 1 µm of coma or trefoil cause a significant degradation of visual acuity from −0.1 logMAR to 0.1 logMAR which refers to 2 lines in a visual acuity chart [12]. Our samples had approximately 0.56 µm of coma and 0.42 µm trefoil in the image quality group 3. Young et al. found that especially defocus and secondary astigmatism affected reading performance more than coma [13]. However, those results cannot be compared directly, due to different pupil sizes and the difference of the visual task. A follow-up study with a smaller measurement aperture will allow comparison to those data. For this we plan to include a different eye-protector model which is used in laboratory environment, where reading is a frequent task.
Our results show a strong agreement between the wave-front technique and the optical bench technique for spherical and astigmatic power measurements. The differences we found can be explained by the intra-rater-reproducibility which is in the range of the measurement inaccuracy of 0.01 D (unpublished data).
Our study had several limitations: The trained observer quantized the spherical and astigmatic power readings in steps of 0.01 D, although an interpolation of 0.005 D might have been possible. The refractive power of higher order aberrations, especially spherical aberration, has an effect on spherical or astigmatic power measurement. This made it difficult to separate spherical powers deviations of 0.005 D (depth of focus). The positioning of the eye protectors was not exactly the same in both devices, which also may explain differences between the measurements.
The derived theoretical model for optical classification resulted in a linear prediction model for the image quality (R2 = 0.998). This can be considered an excellent prediction model, taking into account that we tried do resample a subjective measure factor by objective parameters such as Zernike coefficients. However, additional analyses with different lens models and production parameters showed that this prediction model cannot be directly applied to other lens models since the lens models show different characteristic aberration profiles. The results on the type of characteristic aberrations will help us to create better pass/fail criteria and to investigate the source of the errors in the production process.
5. Conclusions
Eye protectors have to fulfill refractive power as well as image quality requirements in order to be classified as ‘optical class 1’. The subjective optical bench measurement does not distinguish between low and high order aberrations, which may be important for quality control. An objective measurement technique such as wave-front sensing provides detailed data on the aberrations and precise refractive data, the subjective impression of image quality could be reproduced by an objective classification based on wave-front data. Wave-front sensing is a suitable tool for investigating imaging properties of zero-refractive protective eye wear.
Acknowledgments
This work is dedicated to our colleague Dieter Nagengast, who passed away in 2010. The authors wish to thank Gerhard Haubner, Stefanie Fuhrmann, Matthias Reidinger (Uvex Arbeitsschutz GmbH) for performing the measurements. We also want to thank Johannes Pfund (Optocraft GmbH) and Thomas Fröhlich (Laservision GmbH) for seminal scientific discussion and Balazs Gyöngyössy for his help during initial measurements. This work was partially supported by a research grant of the Bayerische Forschungsstiftung (AZ-874-09) and Uvex Arbeitsschutz GmbH, Fürth, Germany.
References and links
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