Using wavefront analysis software to measure the optical power distribution of contact lenses
18-04-2023
SHSWorks is a powerful and comprehensive wavefront analysis software package that allows complete Zernike polynomial analysis, PSF/MTF calculation, laser beam parameter calculation and refractive data. Developed by Optocraft GmbH, a member of the Micro-Epsilon group of companies since 2018, the software is fast and easy to setup using predefined configurations and users benefit from a variety of features such as data logging, advanced reporting and Pass/Fail analysis.
In the ophthalmic market, Optocraft instruments measure refractive data of contact lenses and intraocular lenses (IOLs) and calculate the corresponding power map with a lateral resolution of up to 200 x 200 sampling points. The following application provides information on the use of the different power map features in SHSWorks, as well as some use case examples on contact lenses.
Concept of power maps
In general, a power map provides information on the local power distribution of the optical element under test. Originally, the concept of power maps was used for the description of topological data of the human eye and the closely related optical properties or aberrations to be corrected by a lens. These methods can be easily adapted to represent the optical power distribution of any specimen with unknown topological profile. However, rather than a topological surface, the same calculations can be applied to a measured wavefront or phase distribution.
Definition of power map types
The power map is a 2D array of the local refractive power of the lens. SHSWorks offers different power map types, as shown above (two rays labelled 1 and 2 are shown to better illustrate the equations on the right):
The graph on the left illustrates the calculation of the axial local power Psag and of the refractive local power Pref . The graph on the right shows how the tangential local power Ptan is calculated.
Axial/Sagittal power map
The sagittal or axial power map is calculated from the distances d along the normal vectors of the wavefront to the optical axis as Psag = 1/d. Thus, the sagittal power map is only based on the local slope of the wavefront.
Refractive/Focal power map
The refractive or focal power map is closely related to the sagittal power map. The point of intersection of the surface normal to the optical axis is determined in the same way, but the refractive power map is then calculated using the short side f of the triangle as
Pref = 1/f. The global tilt of the wavefront is always subtracted before calculating the axial and refractive power map.
Instantaneous/Tangential power map
The instantaneous or tangential power map corresponds to the local curvature of the surface in the meridional plane and is calculated using the equation:
Here, p corresponds to the radial coordinate, whereas R denotes the radius of curvature of the wavefront W at the respective position, as depicted in the graphs above.
Local sphere map
The local sphere map is recommended for the analysis of varifocal glasses, but usually not as a representation for contact lens power maps. However, in some cases, the local sphere map can also provide interesting information about contact lenses with a continuous power transition.
Measurement of a multi-focal toric lens
The sagittal power map below belongs to a multifocal toric lens. The image on the left shows the power map including all aberrations. The different power in the two meridians resulting from the toric design is clearly visible. In order to better analyse the zonal structure of this lens, all non-rotational symmetric Zernike terms (result shown above on the right) are subtracted. The annular zones of the lens are now much more evident and provide a more intuitive understanding of the power distribution in each annular zone.
Polynomial- versus spot-based power map algorithms
SHSWorks offers two algorithm options for the power map calculation: spot-based and polynomial-based power calculation. For lenses with a smooth course of the local optical power, the polynomial-based algorithm will provide clearer results. This is because local disturbances such as dust or small defects are not represented in the power map. Instead, the polynomial-based power map shows the overall course. The desired amount of smoothing in the polynomial reconstruction can be controlled by choosing an adequate degree in reconstruction tab of SHSWorks. The quality of the reconstruction can be evaluated by the error function.
The polynomial-based power map is generally a good choice for lenses with continuous designs, whereas for multifocal lenses with discrete steps, the spot-based algorithms are the first choice.
Decentred power profile
If the refractive power profile of a lens is decentred with respect to its optical zone, a double peak will occur at the centre of the power map. SHSWorks detects the rim of the lens and so determines its centre position. For the analysis of lenses with a decentred optical zone, it is possible to laterally shift the entire power profile in a given direction. In the example below, a shift of 0.27mm suppresses the central double-peak in the power map.
Conclusion
In most cases, the spot-based sagittal power map is a good choice and therefore has been chosen as default in SHSWorks.
It is not recommended to use any power map for detection of flaws or aberrations in the shape of the lens. For this purpose, the wavefront is best suited, as power maps are only derivatives of the more immediate wavefront data. In addition, the wavefront offers the possibility of a Zernike decomposition.
When considering diffractive lenses, each zone of the lens generates a separate wavefront. Depending on the lens design, these wavefronts may overlay on the wavefront sensor, so that measurement of a diffractive lens can be difficult or simply not possible.
Accuracy of the power map calculation
The graph below shows the radial sagittal power profile of a meniscus lens, averaged in the azimuthal direction. The orange line results from a direct measurement in transmitted light configuration, as is the case in Optocraft ophthalmic instruments. The blue line results from a very precise measurement (accuracy 2µm) of the curvature radius of the front and back of the same lens. Together with the centre thickness of the lens, these radii were used to model the lens in Zemax. The blue line represents the result of a raytracing simulation. The graph below shows an excellent agreement of the direct measurement in transmission and the simulation based on the measured lens dimensions.
In conclusion, this demonstrates that a direct measurement in transmission correlates very well with the highly precise, indirect measurement based on the curvature radii.
Optocraft SHSInspect instruments are widely used in R&D and production when performance, reliability and efficiency counts most. Based on the state-of-the-art wavefront sensor SHSLab, Optocraft offers measurement modules, turnkey instruments and automated tools for a great variety of applications in the field of optics and optical systems, such as:
- objective lens testing
- testing of optical elements and windows
- surface shape measurement
- inline measurement and automation
Optocraft provide wavefront sensors and inspection systems that are distinguished by their high speed, single-shot measurements, excellent unreferenced accuracy, extreme dynamics and broad spectral ranges. They are also able to measure wavefronts with very strong higher order aberrations. They can measure large tilt angles and strongly defocused beams. They offer high intrinsic stability and reliability, powerful, customisable evaluation software and are versatile and flexible in usage. Optocraft’s systems are in operation in many demanding customer applications.
For more information on SHSWorks and the Optocraft product range, please visit www.micro-epsilon.co.uk or call the Micro-Epsilon sales department on +44 (0)151 355 6070 or email mailto:info@micro-epsilon.co.uk
