OFR manufactures the widest selection of standard, minimum aberration (Best Form) Laser Lenses available from any supplier. Combining quality and theory, these lenses will meet predicted performance within diffraction limit.  We are concerned with the size of the focal spot (the "blur circle" diameter or Airy's Disc). The principles are described in any university level physics text, namely the interplay between spherical aberration and diffraction. 

Specifically, two phenomena occurring:

• Refraction of a ray of light through a lens along with its resultant spherical aberration
• Distribution of optical energy in the focal plane as caused by diffraction.

If there were no such thing as diffraction, then the focal spot would simply get smaller as the focal length increases (or, conversely, as the aperture decreases), corresponding to decreasing spherical aberration.  There is a limit to how small the focal spot can become, even though spherical aberration might approach zero. This is controlled by diffraction, which describes the distribution of energy at the focus. This is Airy's Disc, and is defined as the diameter of the central ring, within which 84% of the energy is contained. 

The two formulas relating to focal spot size are on the front cover of this catalog and below. Thus, the two factors controlling the size of the focal spot are described as:

• Spherical aberration The focal spot size, bs =1.27λf/d derives from the "resolving power" of an optical aperture focusing light from a distant star. The constant 1.27 corresponds to a monochromatic Gaussian beam. In the case of light from a distant star (white light of constant energy density cross-section), the constant is the familiar 2.44. 
• Diffraction The focal spot size is bd = Kd3/f2. K is a constant dependent upon the index of refraction. f is the focal length. d is the beam diameter.

See the formulas on the front cover of this catalog. These are approximations, intended to estimate quickly focal spot size.  We are concerned with the intersection of these two functions, from which we calculate our optimum focal length for any lens with respect to a beam of a specific diameter. Thus, fo = C(d4/λ)Z\c (again, see formulas on front cover). Then, we calculate the two focal spot sizes, b_s and b_d. These will be equal when we use the lens at its "optimum focal length", f_o.  When the beam diameter exceeds the optimum aperture, or the focal length gets shorter, then diffraction is in control, and the focal spot grows rapidly by Kd3/f2.  Conversely, when the beam diameter decreases, or the focal length increases, spherical aberration takes over, and the focal spot increases linearly by f/d.  OFR Best Form (minimum spherical aberration) Laser Lenses will perform to diffraction limit when used within the constraints described by these formulas.

At OFR we manufacture more lenses than any other type of component. Most of the lenses we manufacture are on a custom basis and in large quantities. Therefore, not only do we offer our wide, standard line of off-the-shelf lenses, but we are especially skilled in rapid and precision manufacturing of lenses on a custom basis, in single and low quantities as well as in large quantities.  We manufacture lenses in all standard optical materials. Our largest lens is in the vicinity of 16 inches diameter.

Our current radius tooling and test plate values are also available on our website www.ofr.com. The designer is encouraged to base designs utilizing standard radii values and preferred glasses wherever possible; this will aid in reducing costs and delivery times.

Spherical Radius Tooling (mm)