iPhasematch vs Least Squares Curve Fit

iPhasematch allows you to calculate the phasematching condition of nonlinear wavelength conversion such as SHG or SFM based on published Sellmeier equiations. Downconversion (OPO) can be figured out by the reverse of SFM. It is a subset of the 'Qmix' function of a famous Windows software SNLO by Dr. Arlee Smith. This App does some of what SNLO does on your iOS device. It takes the crystal, two input wavelengths, and temperature and gives the phasematching orientations, effective nonlinear optical coefficients, walk-off angles, angular tolerance and temperature tolerance. In case of SHG, it also gives spectral tolerance. In biaxial crystals, it gives only the phasematching orientations in the principal planes, i.e., either theta=90 deg. or phi=0 or 90deg. Currently supported crystals: BBO, BiBO, CBO, CLBO, LB4, LBO, KBBF, KDP, KD*P, KN, KTP, Mg:LN, Mg:sLN, RBBF, RTP, YAB. NOTE: dn/dT data for LB4 was picked up from discrete data points in the reference and linearly extrapolated. Interface should be intuitive, giving phasematching with a tap of "PM" button,refractive index with "index" button and group index with "Gp.Idx" button, for the given condition (crystal, wavelengths, and temperature). DISCLAIMER: I cannot be held responsible for the result of the calculation it gives. I make every effort to make it accurate, and bug-free, but there could be errors in code. Please just use this on your own discretion.

“Least Squares Curve Fit” is a user friendly, free of charge and free of ads app. User inputs point sets and chooses function types. Utilizing the Least Squares Linear Regression Method, the app calculates best fit curves, reports equations and draws graphs. Point sets can be stored in a table and are available after app is closed. Currently available function types are: 2D: 1. Line. 2. Parabola. 3. Polynomial up to 8th degree. 4. Circle. 5. Conic section (Ellipse or Hyperbola). 6. Trigonometric function as C + A1*cos(ω*x) + B1*sin(ω*x) + … + An*cos(n*ω*x) + Bn*sin(n*ω*x), where user can select n between 1 and 8 and enter any ω. 7. Exponential Function. 8. Bell Curve. 3D: 1. Plane. 2. Sphere. Also, there is an option to choose the Best Fit: the app goes through all the possible shapes and lists them in order from best to worst fit based on residuals. In some cases, when the standard Least Squares method with orthogonal projection does not work, best fit for Line, Parabola, Polynomial and Trigonometric functions can be calculated with SVD. Links to four other free apps by same developers are included in the app: 1. “Matrix Solver Step by Step” Linear Algebra Visual Guide. 2. “Polynomials and Linear Systems” Equation Solver. 3. “GraphMath” Graphing Calculator. 4. “Vectors and Planes” (and Spheres and Ellipsoids) 3D Geometry Guide. Developers hope to get feedback from users at graphmath@aol.com.