## 2 Materials and Methods
### Filters  
Several publications have highlighted the controversy surrounding the use of filters when performing NIMO measurements [9; 10; 14]. The NIMO allows for the application of filters in the center of the radial power map. When working with power maps from projection, the center filtering can be adjusted with various parameters, such as transition distance and kernel size. Although filtering produces smooth power profiles and maps, it can also alter the measurement, which may result in power errors due to the smoothing algorithm.  
The NIMO TR1504 has several calculus options. When calculating the radial power map there is an option to apply a filter in the center of the map. To do so, the user must supply the values of three parameters that control (1) the size of the kernel (defined as the size of the filter kernel employed in processing within the transition distance region) employed to smooth the power map, (2) the radial distance that limits the zone where the filter is applied (only the central portion of the lens should be filtered as it is the zone where the noise is greater), and (3) the distance that defines the circular area used for computing the average power. With this information, the deflectometer produces the MF Map Transition Distance, MF Map PixelWide, and MF Map Filter Kernel Size. When calculating the radial power map of a multifocal lens, a filter is applied in the center of the map. Basically, when the distance between the calculated point and the lens center is inferior to the MF Map Transition Distance, the value is a linear interpolation between the radial power and the local power projected on the radial axis. Local power at a given point is the power deduced from the deviation difference at a distance of \(+\) and \(-\) MF Map Pixel Wide from the point. Once the calculation is performed, a median filter is applied, its kernel being indicated by the MF Map Filter Kernel Size parameter. All these parameters are expressed in pixels and the values are of the integer type [15]. As a result, these filters are smoothing methods, often applied to an input vector, time series, or matrix to generate a smoothed version of the input sequence. These filters, transition distance, and kernel size can be changed from their default values of 20 and 20 to improve their ability to resolve sharp transitions within the power profiles. Both filters are applied in the central part of the  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Lens** & **Power (D)** & **Sys. Error (D)** & **Sys. Error (\%)** & **Rand. Error (D)** & **Rand. Error (\%)** \\ \hline LA1207 & 10.03 & \(-\)4.1\(\cdot\)10\({}^{-4}\) & \(-\)0.004 & 0.002 & 0.02 \\ LA1207* & 10.03 * & 0.03 * & 0.03 * & 0.013 * & 0.13 * \\ LA1213 & 20.08 & \(-\)0.12 & \(-\)0.6 & 0.002 & 0.01 \\ LA1213* & 20.08 * & 0.018 * & 0.09 * & 0.015 * & 0.07 * \\ LA1289 & 33.44 & 0.51 & 1.7 & 0.003 & 0.01 \\ LA1289 * & 33.44 * & 0.47 * & 1.4 * & 0.016 * & 0.05 * \\ \hline \end{tabular}
* The asterisk indicates that the corresponding figures have been computed within the central zone of the lens delimited by a circle of 0.5 mm diameter around the optical center of the lens.  
\end{table}
Table 1: Systematic and random power errors computed from the power profiles.  
map, where interpolations are used to smooth the radial power. According to the options available in the NIMO TR1504 and the papers published with filters, the options assessed were no filter, filter 20/20, and filter 5/10 [14].