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# Spherical Mirror

A spherical mirror is an optical element that reflects light. It has the shape of a piece cut out of a spherical surface, while the back is typically plano. Our spherical mirrors have aluminum coatings and highly polished spherical surfaces, and are ideal for technical OEM visible or IR applications. They have applications in defense and security, medical and agriculture technologies, and environmental surveillance.

The two primary types of spherical mirrors are concave and convex. Concave spherical mirrors have a reflective surface that curves inward. They are converging mirrors and are ideal for focusing light, and they will magnify objects that are close to them. They have a positive focal length, which simply means that the focus of the spherical mirror is between the light source and mirror.  The radius of curvature is also positive; this is the distance between the mirror and the center of the sphere from which it was formed.

Convex spherical mirrors, on the contrary, usually make objects look smaller than they are.  These mirrors are used for expanding an imaging system’s field of view. Concave mirrors has negative focal lengths, which means the focus is behind the mirror.  The radius of curvature is also negative, since the center of the sphere formed by extended the mirror would be behind, not in front of the mirror. Since a concave mirror causes light rays to diverge the image formed is virtual, not real. The rays of light do not actually pass through the point they appear to be originating from. For a convex mirror, the shorter the focal length, the wider the field of view.

## Spherical Mirror Terminology

The principal axis of a spherical mirror is the line that is normal (perpendicular) to the center of the mirror. That central point, where the principal axis enters the mirror, is called the vertex or pole.

The point on the the principal axis which is the same distance from every point on the mirror is known as the center of curvature. The center of curvature is also the center of the parent sphere. The distance from the center of curvature to the vertex is called the radius of curvature.

All light rays striking a concave mirror parallel and near to its principal axis will be reflected through a point on the principal axis, and it is this point which is called the focus or focal point. For a convex mirror, the focus is where the rays appear to diverge from. For either type of mirror, the focal length is the distance along the principal axis from the vertex to the focus.  For a single spherical mirror, the focal length will always be half the radius of curvature.

Note that rays which are both parallel and near to the principal axis are reflected through the focus. The further out the parallel rays hit the mirror, the closer to the mirror their focus becomes. This is the cause of spherical aberration, which can never be completely avoided when working with spherical optics. The paraxial approximation is the mathematical approximation used to idealize our optical system and neglect spherical aberration.

## Manufacturing our Concave Mirrors

At Shanghai Optics we use a special computer controlled sub-aperture tool to manufacture highly precise spherical surfaces, and our careful post-processing to decrease surface roughness and wave. This puts our mirrors a class above similar mirrors manufactured with only traditional methods. Our controlled polishing method and engineering techniques enable us to meet even the tightest specifications.

## Shanghai Optic Custom Spherical Mirrors

If our in-stock curved mirrors do not meet the needs of your application, please call us to discuss a custom order. The Shanghai Optics design team can work with you to determine what specifications that are ideal for your situation and design an optical system that fully meets your requirements. Our factory is equipped with state of the art manufacturing and meteorology equipment, and we run careful quality checks on every optic that is produced in our factory.

## Factory Standard

Our spherical mirrors are manufactured from BK7 with a metallic coating. BK7, Schott borosilicate glass, is high quality optical crown glass with very few impurities.  These mirrors have a surface quality of 40-20, per military standard MIL-PRF-13830B. The clear aperture is guaranteed to be more than 90 percent of the diameter.

Factory Standards:

• Spherical tolerance: λ/4
• Diameter: +0, -0.2mm
• Surface quality: 40-20
• Clear aperture: >90% diameter