Trabajos presentados en el congreso, SPIE Optical Metrology, 2019, Munich, Germany.

**Design of a two-mirror telescope using a free-form surface for the primary mirror**

J. J. Alvarado-Martínez ^{a},
F. S. Granados-Agustín^{a}, S. Vazquez-Montiel^{b}, M. E.
Percino-Zacarias^{a}

and A. Cornejo-Rodríguez ^{a}

^{a}
INAOE, Luis Enrique Erro 1, Sta. María Tonanzintla, Cholula Pue, MEXICO;

^{b}UIEPA,
Los llanos Kilómetro 1, San Andrés Tlayehualancingo, Ahuacatlan Pue, MEXICO.

ABSTRACT

The design of a two-mirror telescope using a free-form surface for the primary mirror, to obtain a compensation of the spherical and coma aberrations, in the entire pupil of the telescope is proposed. In this design, the conic constant (𝑘1) of the primary mirror is a function of the heights, measure from the center to the edge of primary mirror. In this method, we use the exact ray tracing to find the optical path length (OPL) for each ray that intersect the primary mirror at different distances measured from the center of the primary mirror. The OPL is calculated with the sum of the distances that each ray travels until reaching the plane of the image, and the sum of the distances for a paraxial axial ray. From the optical path difference (OPD) of a set of rays, we obtain a set of values of the conic constant that guarantees that the OPD has a value of zero for each incident ray height. With the set of values of the conic constant it is possible to obtain the shape of the surface of the primary mirror.

**Interferometric measurement of local radii of curvature for aspheric
surface using a PDI**

María Elizabeth Percino-Zacarías^{a}, Fermín-Salomón
Granados-Agustín ^{b}, Daniel Aguirre-Aguirre^{b}, Brenda
Villalobos-Mendoza^{b}, Alejandro Cornejo-Rodriguez^{a}

^{a}Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE,
Apdo. Postal 51 and 216,

C. P.72000, Puebla, México.

^{b}Instituto de Ciencias Aplicadas y Tecnología (ICAT), Universidad
Nacional de Autónoma de México (UNAM), Cd. Universitaria, Apdo. Postal 70-186,
C.P. 04510, Cd. Mx, México.

ABSTRACT.

One of the problems that have manufacturers of aspheric and freeform surfaces is the local measurement of the shape, in order to ensure the performance of the surface. In this paper we present an alternative method to measure local radii of curvature of systems with symmetry revolution, using the Point Diffraction Interferometer technique (PDI). To implement this proposal a certified plane wavefront is used as reference light source, and the PDI as sensor element for measuring the local radii of curvature. We proposed to use a PDI due to its high sensitivity because is a common path interferometer and generate interference only when there is an only point a single convergence which is produced from an annular region of the surface, and the annular region is associated to each local curvature center. Experimental results are shown for one aspherical surface with different rates of change in their slopes for each region of the surface, showing the versatility of the proposal and its possible use, including free-form surfaces without symmetry of revolution.

**Measurement of errors by axial misalignment and tilt of the null
screen used in experimental arrangements by de**

**ectometry**

Diana Castán-Ricaño^{a}, Fermín Granados-Agustín^{a},
Andrea Mu~noz-Potosi^{b}, Gabriel Valdivieso-González^{b},
Elizabeth Percino-Zacarias^{a}, Maximino Avendaño-Alejo^{c},
and Alejandro Cornejo-Rodríguez^{a}

^{a}Instituto Nacional de Astrofísica, Óptica y Electrónica, INAOE,
Apdo. Postal 51 and 216,

C. P.72000, Puebla, México.

^{b}FIELDS Group, Universitaria de Investigacion y Desarrollo, Calle 9
No. 23-55, C.P. 680002,

Bucaramanga, Santander, Colombia.

^{c}Instituto de Ciencias Aplicadas y Desarrollo Tecnológico,
Universidad Nacional Autónoma de

México, C.P. 70-186, Coyoacán, México D.F. 04510, Mexico

ABSTRACT

To measure the quality of optical surfaces, one of the most used
methods is the deflectometry. To implement this technique, a screen is used to
choose some incident rays on the surface under test. Subsequently, the
intersection of the rays is measured, after having passed through the surface,
in a detection plane perpendicular to the optical axis. With the coordinates of
the points in the detection plane, the normal vectors are determined in each
point of the surface under test. The process is simple if the incident rays are
chosen in a configuration called null, that is, in the detection plane the
measured points will be distributed in a uniform configuration, rectangular,
circular, radial, etc. In this work we present the numerical simulations,
considering an incident spherical wavefront in the null screen that is placed
at an arbitrary position between the source and the flat surface of an aspheric
lens that was used in the experimental arrangement. In the simulations it is
expected to obtain a uniformly distributed arrangement of spots, which will be
compared with the experimental results.