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Abstract
A wavefront aberration analysis method for measuring spectacle lenses in real-view condition is proposed and verified using experimental apparatus based on the eye-rotation model. Two strategies—feedback positioning and posture adjustment of incident beams and Hartmann-Shack wavefront-aberration sensor calibration at each measurement subarea—are applied to improve measurement accuracy. By simulating the real-view condition, wavefront aberration and user power on the vertex sphere can be obtained. Comparison experiments demonstrate the validity and accuracy of the proposed method and experimental apparatus. Freeform progressive addition lenses are also measured and the results analyzed. The findings provide a possible approach for optimizing the design of spectacle lenses and evaluating their manufacturing and imaging quality.
© 2017 Optical Society of America
1. Introduction
Wearing spectacle lenses is the most popular approach to correct refractive errors in human vision. It poses the advantages of safety, convenience and low cost when compared to other vision correction approaches such as contact lenses, intraocular lenses, and surgical approaches like laser-assisted subepithelial keratectomy (LASEK) or laser-assisted in situ keratomileusis (LASKI) [1–4]. With the progress of advanced computer-aided design and high-precision manufacturing technologies, spectacle lenses with complex surfaces and multi-functions have emerged and attracted growing attention in the optometry industry. For example, aspheric lenses provide fewer aberrations, lighter weight and a thinner appearance than spherical lenses, and freeform lenses, such as progressive addition lenses (PAL), provide variable powers and more comfortable vision correction than bifocal lenses for people with presbyopia [5,6]. The accurate measurement and evaluation of spectacle lenses is essential for optimal vision correction ability and the highest image quality on a subject’s retina [7–9]. The expansion and popularization of freeform and multifunctional spectacle lenses poses a challenge to existing measurement and evaluation methods, while simultaneously requiring new measurement methods with better accuracy, reliability and comprehension [10].
To achieve perfect vision correction, it is necessary to obtain the refraction errors of a subject’s eye accurately, allowing the spectacle lens to be designed and manufactured subsequently to compensate for these errors. The wavefront aberration can be used to demonstrate the total image defection of an imaging system including the eye and spectacle lenses. According to the ISO TC172/SC7 of ophthalmic optics and instruments, the orthogonal Zernike polynomials can express the wavefront aberration of an eye. This wavefront aberration can be divided into lower order aberrations (LOA) including defocus, astigmatism, distortion, etc., and higher order aberrations (HOA) including coma, spherical aberration, trefoil aberration, etc [11]. The development of self-adaption optics and freeform optics manufacturing technology raises the possibility of achieving zero wavefront aberration (diffraction-limited) correction ability, allowing supernormal vision to be achieved [12,13]. As a result, the current resurgence of research interest in ophthalmology and refractive surgery focuses primarily on the measurement and correction of HOA in the 3rd, 4th and 5th order as well as the common LOA of defocus and astigmatism [14,15].
Conventionally, the most widely used device for the measurement of spectacle lenses is the lensometer/focimeter, which measures the paraxial back vertex focal length of the spectacle lenses [16]. The lensometer/focimeter measures small areas at several locations on the spectacle lenses’ surface and provides limited parameters, such as the spherical power, the cylindrical power and the axis. However, when measuring freeform or multifunctional spectacle lenses, it is necessary to obtain a greater range of optical parameters over the whole lens surface so that the vision correction ability and image quality can be accurately evaluated. Thus, both the LOA and the HOA of the spectacle lens have to be measured so that the distribution and the total amount of the wavefront aberration can be measured, allowing estimation of the lens’ compensation to be consistent with the wavefront aberration of the subject’s eye. Several measurement methods and experimental devices have been developed to measure freeform spectacle lenses, and to evaluate their vision correction ability and image quality by measuring the complete distribution of wavefront aberrations over the whole lens surface. These methods include the coordinate measurement machine method to obtain the surface profile of the lens [17], the Moiré deflectometry or reflection grating method [18,19], the phase-measuring deflectometry (PMD) [20], the interferometer method [21], and the Hartmann-Shack wavefront aberration testing method [22,23]. The Hartmann-Shack wavefront aberration method can be employed to directly obtain the wavefront aberrations of the incident light after passing through the spectacle lens; it has been widely used in measuring the wavefront aberration of the human eye and spectacle lenses, contact lenses and intraocular lenses [7,12].
In addition to the necessity of measuring the complete wavefront aberration and its distribution over the whole spectacle lens’ surface, the third requirement for spectacle lens measurement is the real view condition, in which the orientation of both the spectacle lens and the eye is considered, as the spectacle lens functions cooperatively with the eye to correct vision. In the real view condition, the spectacle lens is kept still and the eye is rotated around its center of rotation. Consequently, parallel beams of incident light pass through different subareas on the spectacle lens before being focused on the macular fovea of the retina when the eye gazes at targets with differing view angles. At one-shot viewing, although many incident beams pass through subareas over the entire surface of the spectacle lens and converge on the whole retina surface, the image on the macular fovea is the sharpest and clearest. The corresponding small subarea on the spectacle lens therefore acts as the main vision correction mechanism. As a result, when different subareas of the spectacle lens are measured, the corresponding incident beams and the eye’s rotation should also be taken into account. Much research has been carried out to measure spectacle lenses in real view conditions with consideration of both the spectacle lenses and the eye. Vargas used the deflectometric method to measure the user power for ophthalmic lenses while considering the ophthalmic lens-rotating eye scheme [24]. Villegas and Zhou utilized the Hartmann-Shack wavefront aberration method and built experimental apparatus to measure the spectacle lenses in normal or real view conditions by translating the spectacle lens’ position and rotating its posture during measurement [25–28]. This kind of measurement is referred to as a lens motion based method. However, simulating the eye’s rotation with the motion of the spectacle lens is not the same as the real view condition. If the rotation center of the spectacle lens is not accurately positioned and translated when the relative movement transformation method is used, position errors are introduced in the relative distance and relative angle between the spectacle lens and the eye when compared with the real view condition. This has the effect of introducing refraction errors, leading to wrong measurement results. Another drawback of using the Hartmann-Shack wavefront aberration measurement method is that the Hartmann-Shack wavefront aberration sensor (HSS) has to be calibrated at each subarea on the spectacle lens surface after varying the position of the spectacle lens and the incident beam direction. This is done to eliminate systematic errors in the measured optical path and to ensure only the wavefront aberration of the spectacle lens is obtained.
In this paper, an eye rotation based model considering the spectacle lenses, the eye and the incident beam in the real view condition, is developed and demonstrated. A prototype experimental apparatus based on the Hartmann-Shack wavefront aberration method is then constructed, which can simulate the real view condition. This is achieved by allowing the eye (the HSS) to rotate around its center of rotation about two axes, with the primary incident beam being rotated and translated to the corresponding subarea on the spectacle lens, with the spectacle lens kept stationary during measurement. Strategies of feed-back positioning and posture adjustment of the incident beams as well as calibration of the HSS at each measurement subarea are applied to eliminate systematic errors during the measurement process and to improve the measurement accuracy. Experimental measurement of a spherical single vision lens is then carried out using the proposed method on the self-developed experimental apparatus. The surface distribution of wavefront aberration inside the measurement margins is obtained and LOA and HOA are analyzed. The measured distribution of user power is compared with measurement results from commercial lensometers. The consistency between measurements at the center position demonstrates the validity and accuracy of the proposed method and of the prototype experimental apparatus. The reasons for the observed gradual variation of the measured user power on the vertex sphere, including the appearance of a concentric circle, are analyzed. Finally, the experimental measurement of a freeform PAL is carried out and the measurement results are presented and analyzed. The experiment results demonstrate that the proposed wavefront aberration measurement method based on the eye rotation model which simulates the real view condition can provide accurate measurements of spectacle lenses.
2. Eye rotation based approach
Figure 1 shows a diagram of the eye rotation based model in the real view condition with a consideration of incident beams, the spectacle lens and the eye. It demonstrates how the incident beams from a viewing object are refracted and corrected by the spectacle lens and then imaged on the retina of the eye. Multiple incident beams from the entire field of view (FOV) of the eye pass through the spectacle lens, the cornea and the lens of the eye, and form images on the retinal surface. Among these beams, the primary incident beam from the fixation target T forms the clearest and sharpest image at T” on the macular fovea of the retina surface, which corresponds to the eye position with vertical view angle θ and horizontal view angle ω. At the same time, the functional vision correction subarea on the spectacle lens surface is determined, as shown in the lower right figure in Fig. 1. In effect, when the spectacle lens is worn by the user, its main working area can be divided into many continuous small subareas corresponding to different view angles (θ and ω). This means it is no longer necessary to obtain the one-shot wearer power of the spectacle lens but it is possible to measure the “user power” or “wear power” regionally, corresponding to the different view angles of the user’s eye. These user-oriented measurements also provide another way to evaluate the design, manufacture and imaging qualities of spectacle lenses. The back focal point of the spectacle lens must always be located at the far point of the eye when the eye rotates to different view angles. In other words, the far point sphere of eye remains coincident with the back focal sphere of the spectacle lens. For example, the point T' on the far point sphere in Fig. 1 conjugates with T” on the macular fovea. The vertex sphere VS is the sphere centered on the eye’s center of rotation (COR), O, and extends to the spectacle lens’ back surface vertex. The distance between the far point sphere of the eye and the vertex sphere remains constant when the eye gazes in different directions, and can be expressed by 1/D, where D is the power of the spectacle lens in diopters. The power measured on the vertex sphere therefore represents the user power more accurately and is a more important measurement than the power on the back surface of the spectacle lens, the measurement usually detected by a focimeter/lensometer. The measured wavefront aberrations on the vertex sphere are also of higher importance than the wavefront aberrations on the back surface of the spectacle lens.
An experimental apparatus based on wavefront aberration method was built to measure spectacle lenses by simulating the real view condition in accordance with the eye rotation based scheme. As shown in Fig. 2, the experimental apparatus could be divided into three main parts, the light source which simulated the primary incident beams, the spectacle lens holder which held the spectacle lens fixed in place during measurement, and the optical 4F (4 focal length long) system and Hartmann-Shack wavefront aberration sensor (HSS) which simulated the eye’s rotation and detected the wavefront aberrations of the spectacle lens. A diode laser LD (λ = 520 nm) emitted a point-source beam of light. The lenses L1 and L2 caused beam expansion and collimation, respectively. The collimated light, which had zero wavefront aberrations, passed through the aperture, AP, and functioned as the primary incident beam. The diameter of the primary incident beam could be adjusted by varying the aperture AP. The LD, L1, L2 and AP functioned together as the light source in the experiment. The light source was installed on a precision 4-axis motion platform, which translated the light source in the X” and Y” directions and rotated it in Rx” and Ry” directions. The rotation center of the 4-axis motion platform, O”, was located at the center of the lens L2. While the spectacle lens was held fixed on the spectacle lens holder during measurement, its position in Z direction could be adjusted by the Z manual translation stage. Lenses L3 and L4 functioned as the optical 4F system, with the measurement surface of the HSS located at the back focal point of L4 and the back surface vertex point of the spectacle lens O' located at the front focal point of L3. The optical 4F system and the HSS were combined together in a casing pipe which not only caused them to move together but also shielded the optical system from ambient light. The casing pipe was fixed on a precision 2-axis motion platform, which rotated in the Rx and Ry directions. The 2-axis motion platform simulated the rotation of the eye in the horizontal (Ry) and vertical (Rx) directions. The rotation center of the 2-axis motion platform, O, was located at the radial center of the casing pipe. Before taking measurements, the distances d1 and d2 had to be accurately adjusted. First, the distance d1 from O' to O was adjusted by the Z manual translation stage of the spectacle lens holder in Z direction to make sure it equaled the sum of the vertex distance (measured from the back surface vertex point of the spectacle lens to the corneal apex) and the eyeball radius (measured from corneal apex to COR). The vertex distance was measured by the optometrist when the patient’s eye viewed the primary position. The position of the casing piping along the optical axis in Z direction was then adjusted to ensure that the distance d2 equals the focal length of L3. This ensured that when the 2-axis motion platform rotated around Rx and Ry axes, the measurement sphere of the HSS was conjugate with the VS, and accurate wavefront aberrations and the user power of the spectacle lens on the VS could be obtained.
The performance of the precision 4-axis and the precision 2-axis motion platforms was evaluated using a laser interferometer (SIOS SP 2000-TR) and a displacement sensor (Optex CD5-L25A). The resolution, absolute accuracy and repeatability of the 6 single axes and 2 rotation centers of O” and O was measured for calibration and the results are presented in Table 1. It should be noted that the accuracies of each individual single axis differed only slightly, and as such the parameters displayed in Table 1 are the worst ones obtained. The principle of the HSS has been extensively described elsewhere [12,22]. The precision motion platforms and the high-performance HSS guarantee that the following measurements of spectacle lenses are accurate.
Table 1. Evaluation of the Motion Platforms
3. Experiment
3.1 Measurement approach
Figure 3 shows the measurement procedure of the prototype experimental apparatus.
Step 1. Firstly, the distances d1 and d2 are precisely adjusted. d1 is set according to the prescription of the subject, and d2 is set to be equal to the focal length of L3. Next, the spectacle lens is removed from the lens holder and the light source is carefully positioned at the radial center of the casing pipe to ensure that the incident beam is located at the CCD center of the HSS. Here, and in following measurements, we assume that an incident beam located at the CCD center of the HSS simulates the action of an incident beam focused at the macular fovea of the eye. The optimal movement parameters of the 4-axis and 2-axis motion platform, such as the motion steps and speed, and the measurement parameters of the HSS, such as the CCD resolution and the pupil diameter, are then selected and set according to the measurement requirements.
Step 2. The planned coordinates of the measurement subareas on the back surface of the spectacle lens are calculated. Figure 4 shows an example of the coordinate distribution of the planned measurement subareas in the X'Y' plane (Z' = 0) of the spectacle lens coordinate system X'Y'Z' defined in Fig. 5. The pupil diameter is 2 mm, the distance between each measurement subarea is 2.2 mm, and there are 109 measurement subareas inside the measurement margin with 26 mm diameter and corresponding view angle of ± 22.2 °. Then, according to the geometrical relationship between the three parts of the experimental system as shown in Fig. 5, the corresponding theoretical motion coordinates of the 4-axis and the 2-axis motion platform can be calculated using Eq. (1), where x' and y' are the coordinates of the center of each planned measurement subarea, ω and θ are motion angles of the 2-axis motion platform which simulates the horizontal and vertical view angles of the eyeball. ω” and θ”' are the motion angles of the 4-axis motion platform which simulates the corresponding angle change of the primary incident beam. ω” and θ”' have the same magnitude as ω and θ but reversed direction. The x” and y” are motion displacements of the light source in the X” and Y” directions respectively.
In our experimental system, both the Ry” and the Ry rotation stages in the 4-axis and the 2-axis motion platform are fixed on their corresponding Rx” and Rx rotation stages. This means that if the Ry rotation stage rotates first, the position of the Rx rotation stage would not change. Thus, the angle ω and θ can be calculated by Eq. (1).
Figure 6(a) shows the calculated theoretical motion angles, ω and θ, of the casing pipe corresponding to the planned measurement subareas shown in Fig. 4. The calculated theoretical x” and y” displacements of the light source can be seen in Fig. 6(b). The angle of ω” and θ”' at each displacement of x” and y” have the same value as the angle ω and θ but with reversed angle direction.
Step 3. Alignment errors, positioning errors, and motion errors are inevitable while using the experimental apparatus. The location of the incident beams would therefore shift from the CCD center of the HSS when different subareas are measured. To counter this, the calculated theoretical motion coordinates in Step 2 have to be feed-back adjusted inside its limited neighbor area to make sure that the incident beam is located at the CCD center of the HSS when each subarea is measured. The position of the incident beam on the CCD of the HSS is used as the feed-back adjustment reference. The feed-back adjustment finishes for each measurement subarea when the incident beam center coincides with the CCD center of the HSS, or when their position difference is smaller than a predefined threshold. During feed-back adjustment, the angles ω and θ at each measurement subarea are held constant, only the angles ω” and θ”' and the displacements x” and y” are adjusted. The real motion coordinates of the displacement x” and y” after feed-back adjustment are shown in Fig. 6(b). In the following experiment, the light source was moved to the real motion coordinates when each planned subarea is measured.
Step 4. As the posture of the light source and the casing pipe are different at each measurement subarea, the HSS has to be calibrated to eliminate the wavefront aberrations due to the systematic errors of optical path at each measurement subarea. The calibrated reference files of the spot’s positions on the CCD of HSS at each planned measurement subarea can be generated and saved. In order to test the validity of the calibration results, the wavefront aberrations at each planned measurement subarea are measured without the spectacle lens. Figure 7(a) shows the wavefront aberration of incident beams at each measurement subarea with only one calibration at the center subarea. The PV value of wavefront aberration of each subarea is larger than 60 nm, and the PV value of all measurement areas is 160 nm. Figure 7(b) shows the wavefront aberration of incident beams at each measurement subarea following calibration of the HSS at every subarea. It can be seen that the PV value of each measurement subarea is now smaller than 20 nm, proving the validity and effectiveness of the calibration process at each planned measurement subarea. The PV value of all measurement subareas is smaller than 40 nm. Because of repetitive position errors of the 4-axis and 2-axis motion platforms when long range displacements and large angles are involved, the errors in the calibrated wavefront aberration cannot be entirely removed.
Step 5. The spectacle lens is reinstalled on the spectacle lens holder. The measurement of wavefront aberration on the vertex sphere can then be carried out. At each measurement subarea, the corresponding calibrated reference file obtained in Step 4 is first loaded, allowing only the wavefront aberration caused by the spectacle lens to be obtained. Finally, not only the user power, but also the higher order wavefront aberrations of the spectacle lens on the vertex sphere in the real view condition can be obtained.
3.2 Experiment for measuring spherical single vision lens
Experiments to measure an uncut spherical single vision spectacle lens SP1 were carried out. The SP1 had a marked value of SPH: −2.50 D and CLY: −0.00 D on its package.
The spherical power of SP1 was first measured using two different commercial auto lensometers (Nidek LM-990A and Topcon CL-100). The spherical power at 20 locations was measured by the two commercial lensometers along different radial directions of the SP1, from the geometrical center to its margin. The measured spherical power was −2.50 ± 0.02 D, and the measured cylindrical power was −0.00 ± 0.02 D. These results demonstrated that the SP1 was well designed and manufactured to strictly fulfill the measurement requirement of ISO 8598-1:2014 [16].
Following the aforementioned measurement steps, the SP1 was measured using the prototype experimental apparatus by simulating the real view condition. Figure 8 shows the wavefront aberrations of the 109 measured subareas inside the measurement margin with 26 mm diameter. Each measurement subarea had a pupil diameter of 2 mm, and the separation between two adjacent measurement areas was 2.2 mm. The distances d1 and d3 were set to be 27 mm and 56 mm respectively. The Zernike fitting order of the HSS was set to 4. It can be easily seen that the measured wavefront aberrations show a uniform appearance of circular shape with raised center and that the minus defocus occupies the main portion of the total amount of wavefront aberrations in each individual measurement subarea. However, it is difficult to distinguish differences in the wavefront aberrations between subareas. The wavefront aberrations of the center and corner subareas were therefore decomposed using a set of standard Zernike functions. Figure 9 shows the Zernike coefficients of each Zernike component of the wavefront aberrations at the two subareas. It can be seen that the defocus components occupy the main portion of the wavefront aberrations except the piston component, the tip component and the tilt component which rarely have any significance in wavefront aberration analysis. The defocus component in the center subarea is larger than that in the corner subarea, but the astigmatism components of the corner subarea are larger than those at the center, which is mainly caused by oblique astigmatism. The coma component is the main portion of the higher order aberrations, but the total amount of higher order aberration components is negligible when compared with that of the lower order aberrations.
From the wavefront aberration, the equivalent spherical power and the equivalent cylindrical power can be calculated using Eq. (2) [29,30]
where r is the pupil radius and Cn is the coefficient of nth Zernike mode. Figure 10 shows the distribution of equivalent spherical power (Fig. 10 (a)) and equivalent cylindrical power (Fig. 10 (b)) inside the measurement margin of SP1. The spherical power at the center area is −2.50 ± 0.01 D, and the cylindrical power at the center area is −0.00 ± 0.025 D, which show good agreement with the measurement results from the two auto lensometers and the values marked on the lens’ package. These results demonstrate the validity and accuracy of our proposed measurement method and of the self-developed experimental apparatus working in simulating the real view condition. It can be seen that both the distributions of spherical power and cylindrical power in Fig. 10 have the appearance of concentric circles with increasing or decreasing values. In other words, the single vision spectacle lens no longer displays the property of consistent single vision but instead shows gradually varying power in the real view condition. One reason is that in our experimental apparatus, the wavefront aberrations on the vertex sphere are measured, and the separation between the VS and the back surface of the spectacle lens gets larger when the view angle increases, which can be seen in Fig. 1. This separation introduced differences between the user power measured by our system and the power measured by lensometer method. Another reason comes from the difference between the way corrected incident light is received by our method and by the lensometer method. In the lensometer method, whether operating in the infinite-on-axis (IOA) mode or the focal-point-on-axis (FOA) mode, the propagation directions of incident light from all measurement subareas are different from those in the real view condition, with the exception of the geometrically central subarea.The phenomenon of gradual power variation can also be found in normal life when a single vision spectacle lens is worn by a subject. For example, when a myopia patient wears a set of short-sighted glasses, viewing an object through the center of the glass results in a clearer and sharper image than viewing through the non-central areas of the glass at a larger view angle. This kind of image quality disparity is more prominent with higher power spectacle lenses. The basic reason behind this kind of defect is rooted in the design of spectacle lens, which has to fulfill the requirements of focimeter measurement methods and standards.
As a result, the proposed wavefront analysis method which considers the real view condition and the resulting measurements might provide a way to modify the design of the single vision lens. In other words, the single vision lens could be designed with the appearance of gradual power variation but the function of constant single power in the real view condition.
3.3 Measurement of a progressive addition lens
After the experiment to measure the SP1, the SP1 was removed and a progressive addition lens, PAL1 (Make and model: Luomeng Optical, Clever J150), was placed in the spectacle lens holder. An experiment to measure PAL1 was carried out with the same experimental parameters as used to measure the SP1. The PAL1 had marked values of SPH: −1.50 D, ADD: + 300 and CYL: −0.00 D on its packaging. Some locations on the lens’ distance zone, near zone and reference point of its corridor area were first measured with the two commercial lensometers. The measurement results were consistent with the marked values.
The PAL1 was then measured on the prototype experimental apparatus. Figure 11 shows the wavefront aberrations of PAL1 inside the measurement margin with 26 mm diameter. The boundary between the distance zone, the near zone and the two peripheral zones can easily be distinguished from the wavefront aberrations of each measurement subarea. Wavefront aberrations of five representative measurement subareas of the distance zone F, the near zoneN, the center zone C, the left peripheral zone L and the right peripheral zone R were decomposed using a set of standard Zernike functions. Figure 12 shows the Zernike coefficients of each Zernike components of the wavefront aberrations in the five representative subareas. The piston component, the tip component and the tilt component, which rarely have any significance in wavefront aberration analysis, are not displayed in Fig. 12. It can be seen that in the distance zone, the minus defocus component is dominant, but in the near zone, the positive defocus component comprises most of the total wavefront aberrations. The astigmatism components of the distance and the near zone are very small. In the center zone, the amount of all wavefront aberration components almost equals zero, because this location is the prism reference point where parallel incident beams undergo no refraction. It can be seen that the peripheral zones have the largest amount of aberrations of all the zones. The higher order aberrations occupy a very small portion of the total aberrations in each measurement subarea.
Figure 13 shows the distribution of the equivalent spherical and cylindrical power of PAL1, which were both calculated using Eq. (2). It can be seen that the spherical power in the distance zone and the near zone gradually changes when the view angle gets larger because PAL1 was measured in the real view condition. The peripheral zone of the nasal side has larger wavefront aberrations than the peripheral zone of the temporal side, which fulfills the wear and design requirements of progressive addition lenses. The dashed lines in Fig. 13 demonstrate the approximate horizontal position of PAL1 which was defined by two engraving markings on its front surface. Figure 14 shows the spherical power and cylindrical power change of the center line along the Y' direction. It can be seen that the PAL1 has a corridor length of about 11 mm within the power addition range of ADD + 300. The cylindrical power has a good uniformity along the center line. From Fig. 13(b), it can be seen that the PAL1 has an average corridor width of 4.2 mm within the cylindrical power change range from −0.00 D to −0.50 D.
4. Conclusions
This paper presents a wavefront aberration analysis method for measuring spectacle lenses with simulated consideration of the real view condition. Experimental apparatus has been built based on the proposed measurement method. Two strategies, namely feed-back positioning and posture adjustment of the incident beams and calibration of the HSS at each measurement subarea, have been applied to eliminate the systematic errors arising during the measurement process and to improve the measurement accuracy. In comparison with the conventional lensometer/focimeter measurement method, the proposed method achieved both the LOA and HOA wavefront aberration measurement inside the entire measured surface, and the accurate spectacle lenses measurement in real view condition. The user power and the wavefront aberrations on the vertex sphere were obtained. Experimental results of the measurement of a spherical single vision lens demonstrated the validity and accuracy of the proposed method and the self-developed apparatus. The proposed method was also successfully applied to the measurement of a progressive addition lens, and the spherical power distribution and the cylindrical power distribution of the whole measured area were displayed. The higher order aberrations were also obtained. The measurement results provide a possible approach for the comprehensive analysis and evaluation of spectacle lenses. It is expected that the measurement results can be applied to optimizing the design of spectacle lenses, evaluating lens manufacturing quality and determining the imaging quality of spectacle lenses.
In this paper, the measurement range was only limited by the motion range of X” and Y” displacement stages. Whole surface measurement of spectacle lenses could be realized in future work by applying displacement stages with a larger range of motion. Further error analysis, comparison experiments and imaging quality evaluation research based on the proposed method and experimental apparatus can also be carried out.
Funding
National Natural Science Foundation (NSFC) (61635008, 51320105009, 91423101); National Key Research and Development Program (2016YFB1102200); Postdoctoral International Exchange Project of National Postdoctoral Management Committee of China; ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (B07014).
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