Free System of Spherical and Coma Aberrations by Use Aspherical and Diffractive Surfaces

Today, the use of special optical elements for aberrations control is more and more common because these elements reduce the weight and volume of the optical system but the design of these elements is complicated and it is more complicated if we like to use an analytical way; also, in many cases, after an analytic process we must to use an optimization routine with some optical design program. In this work we propose an analytic method to design systems free of spherical and coma aberrations using an aspherical and diffractive surfaces (hybrid element). We analyzed the form of the back principal plane to different shape factor considering the spherical aberration corrected and no corrected. We use the aspherical surface to correct the coma; we obtain this condition curving the back principal plane and centered it on the back focal point. The diffractive element is used to correct the spherical aberration by apply an exact ray trace, and we use the diffractive coefficients as variables. We find these coefficients by solve a first degree equations system. We apply this method to design systems with two surfaces with the object at infinity and with monochromatic light. The last surface is the aspheric surface and also in this surface we put the diffractive element. With our procedure we do not need an optimization procedure.