Averaged and Integral Characteristics

These characteristics can be monitor in the course of analysis as well as during the design process.

It is possible to monitor minimum and maximum values as well.

Analysis –> Integrated values and characteristics

Fig. 1. By clicking Integrated values and characteristics, Integral, Values window opens.

Fig. 2. Color target: color coordinates are specified CIE xyz (1931) color space.

Fig. 3. Integral target: solar direct transmission should be maximized. The details are here.

Fig. 4. Variations of the color coordinates of the designed coating (reflectance and back side reflectance) with respect to the incidence angle. Crosses show target values.

Fig. 6. By default, total merit function value is calculated. Using [+] and [x] buttons you can add or remove desired integrals/averaged values. The values are chosen from the pop-up list. 

Fig. 7. Integral component of the merit function, \(MF_{int}\) is added for the calculation.

OptiLayer allows to specify combined targets and optimize the design with respect many criteria simultaneously.

Fig. 8. Color component of the total merit function is being added. You can monitor the MF Color taking or not taking the weights into account.

Integral weights can be specified in a special Target Weight window ( Data –> Target Weights) or directly in General Information window (Fig.  9).

Fig. 9. Specification of target weights directly in General Information window.

Fig. 10. Color component of the total merit function is added. Target weight of 0.5 is taken into account.

Total merit function MF takes the form:

\[ MF^2=0.5\cdot MF_{color}^2+MF_{int}^2 \]

All required spectral weights are to be specified in advance through integral target option (see Integral Target).

As in Integral Target, there are two check boxes: Normalized and Use Source/Detector. Check or uncheck these boxes affects the integral calculations. Generally, when both boxes are checked, the integral \(F\) is calculated in the following way:

\[ F=\frac{\int\limits_{\lambda_d}^{\lambda_u} W(\lambda)D(\lambda) S(\lambda) C(\lambda)d\lambda}{\int\limits_{\lambda_d}^{\lambda_u} W(\lambda) S(\lambda) D(\lambda)d\lambda},\]

where \(\lambda_d\) and \(\lambda_u\) are boundaries of the wavelength interval of interest, \(W(\lambda)\) is a given weight function, \(S(\lambda)\) is a spectral characteristic of a coating, \(D(\lambda)\) and \(S(\lambda)\) are spectral distributions of the detector and light source, respectively.

Fig. 11. Integral transmittance with normalized relative spectral distribution of illuminant D65 multiplied by the spectral luminous efficiency is specified.

Fig. 12. Choice of the CIE L*a*b* color coordinates for calculation.

You can specify reflectance, back side reflectance, or transmittance; polarization states, and incidence angle.

Integral calculations are performed in the stack mode as well.

Fig. 13. You can calculate and monitor average values as well as maximum/minimum of spectral characteristics over a specified wavelength range.

Fig. 14. It is also possible to display and monitor averaged spectral characteristics as well as their maximum/minimum over a specified angular range.

Fig. 15. Reflectance data averaged over the visible range and the angular range.

Computations of 2D average values is more time-consuming, thus it is recommended to select a moderate number of points for each of dimensions.

It is possible to adjust font type, size, font color and background color using corresponding toolbar controls.

Also it is possible to change the number of digits to display and to select scientific format when necessary (use [E±] button for this purpose).

You can save your style using Save Style as Default and then Apply Default Style in another problem directory (starting from Version 12.83).

Of course, you can turn back to the Build-in Style.

Fig. 16. Using the right mouse button, you can open a sub-menu allowing you to save and restore styles.