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Lens Tutorial

Selecting the Proper Lens

Lenses are subject to numerous types of aberrations; chromatic aberration and spherical aberration are two common examples. By properly choosing the lens design or using multi-element systems, the effects of aberrations can be decreased and the performance of the system can be improved. Many of Thorlabs lens styles are available in multiple high-quality optical materials; once a lens type is chosen, the substrate and/or antireflection coating can be chosen for a particular wavelength region.

Spherical Singlets

Spherical singlets are a good option for many applications where aberrations are not a great concern. Thorlabs offers several singlet designs: Plano-Convex, Bi-Convex, Plano-Concave, and Bi-Concave. Each of these lenses is suited for different applications.

Plano-Convex Lenses
Plano-Convex lenses are best used where one conjugate point (object distance or image distance) is more than five times the other. The performance of this lens shape is near best-form for either focusing collimated light or for collimating a point source. Plano-convex lenses can be subject to some spherical aberration, which can be reduced by using a multi-element system as described below.
Plano-Convex Diagram
Plano-Convex Lens
Bi-Convex Lenses
Bi-Convex lenses perform best when the object and image are on opposite sides of the lens and the ratio of the object to the image distance (conjugate ratio) is between 0.2 and 5 or when used to create a virtual image from an object.
Bi-Convex Diagram
Bi-Convex Lens
Plano-Concave Lenses
Plano-Concave lenses have a negative focal length and are typically used to diverge collimated beams of light in instruments like Galilean-type beam expanders or telescopes. The spherical aberration introduced into the wavefront by a plano-concave lens is negative, and as a result, the lens can be used to balance the positive spherical aberration introduced by positive focal length singlets.
Plano-Concave Diagram
Plano-Concave Lens
Bi-Concave Lenses
Bi-Concave lenses have a negative focal length and are commonly used to increase the divergence of converging light.
Bi-Concave Diagram
Bi-Concave Lens

Figure 1: Multi Element Lens System
Figure 1: Aberrations may be reduced by using multi-element systems

Multi-Element Lens Systems

Figure 1 shows the performance gains that can be achieved by using multi-element lens systems. For example, a single element plano-convex lens with a focal length of 50 mm produces a spot size of 240 µm (Figure 1a). By combining two plano-convex lenses, each with a focal length of 100 mm, for an effective focal length of 50 mm, the focused spot size is decreased to 81 µm (Figure 1b).

Meniscus Lenses

An even better option, however, is to combine the f = 100 mm plano-convex lens with a positive meniscus lens with a focal length of 100 mm. Positive meniscus lenses are designed to minimize spherical aberration. Meniscus lenses have one convex and one concave surface. When used in combination with another lens, a positive meniscus lens will shorten the focal length and increase the numerical aperture (NA) of the system. Figure 1c shows the results: the focused spot size is reduced to 21 µm, and the transverse and lateral aberrations are also greatly reduced. Note that the convex surfaces of both lenses should be facing away from the image.

Positive Meniscus Diagram
Positive Meniscus Lens

 

 

 

Negative meniscus lenses are commonly used in beam expanding applications since they increase the divergence of the beam without introducing significant spherical aberration. Combining a negative meniscus lens with another lens increases the focal length and decreases the NA of the system.

Negative Meniscus Diagram
Negative Meniscus Lens

Achromatic Doublet Ray Diagram
Achromatic Doublet Lens

Achromatic Doublet Lenses

Achromatic doublets offer several advantages over simple singlet lenses. These include a minimization of chromatic aberration, improved off-axis performance, and smaller focal spots. For any application with demanding imaging applications or laser beam manipulation needs, these doublets should be considered.

Figure 2: Focusing White Light
Figure 2: Focusing white light with a plano-convex and an achromatic doublet lens

Nearly Constant Focal Length Across a Wide Range of Wavelengths

Since the index of refraction of a material depends upon the incident wavelength, a single lens will have a blurred focal length and circle of least confusion (spot size) when using a white light source. This phenomenon is known as chromatic aberration. An achromatic doublet can partially compensate for chromatic aberration since it is a combination of two lenses, each with a different index of refraction, thus leading to a partial cancellation of this aberration. Figure 2 shows the effect on focal length for a number of different wavelengths incident on both a plano-convex singlet and achromatic doublet. The circle of least confusion is reduced from 147 µm to 17 µm by replacing the singlet with the achromatic doublet.

Achieve a Tighter Focus for Monochromatic Light

Achromatic doublets also have other advantages over single lens designs for applications with monochromatic light. For example, Figure 3 compares the focusing of a monochromatic beam by a plano-convex lens and an achromatic doublet. As can be seen, the circle of least confusion for the doublet is 4.2 times smaller than that from the singlet. 

Figure 3: Improved Focusing with Achromatic Doublet
Figure 3: Focusing a monochromatic beam with both a plano-convex and achromatic doublet lens
Figure 4: Inproved Off-Axis Performance
Figure 4: Off-axis performance for a plano-convex and an achromatic doublet lens

Superior Off-Axis Performance

The performance of achromatic doublets is also not as compromised as it will be for a singlet lens if the beam is not propagating through the exact center of the lens. Figure 4 shows two 25 mm diameter, 50.0 mm focal length lenses, one of which is a plano-convex spherical singlet and the other is an achromatic doublet. Each lens has one beam propagating along the optical axis and another propagating parallel to the axis but offset by 8 mm. Both lateral and transverse aberrations are reduced for the achromatic doublet; the lateral displacement of the focal points is over six times smaller while the circle of least confusion is also significantly smaller.


Figure 5: Best form aberration performance
Figure 5: Spherical aberration and coma vs. front surface curvature.

Best Form Lenses

Best Form lenses are ideal for use at infinite conjugates in high-power applications where achromatic doublets are unsuitable due to the cement between elements. These lenses are designed to minimize spherical aberration and coma (an aberration introduced for light not on the optical axis) while still using spherical surfaces to form the lens. Each side of the lens is polished so that it has a different radius of curvature. Figure 5 shows a plot of coma and spherical aberration as a function of the curvature of the front face of a lens (the curvature is the inverse of the radius of curvature). The minimal spherical aberration nearly coincides with the zero coma point; the curvature where this minimum occurs is the basis for a “best form” design.

Best-Form Lens
Best-Form Lens

Aspheric Lenses

Aspheric lenses offer diffraction-limited spot sizes, an advantage over achromatic doublets. While individual spherical lenses can refract light at only small angles before spherical aberration is introduced, aspheric lenses are designed with curved surfaces which deviate from a sphere. This deviation is designed to eliminate spherical aberrations when light is refracted at large angles. Aspheric lenses have two important applications: laser diode collimation and fiber coupling.

Collimating Laser Diodes
Figure 6: Collimating a laser diode output with an aspheric lens

Collimating Laser Diodes

In laser diode systems, difficulties with aberration correction are compounded by the beam’s high divergence angle. Because of spherical aberration, three or four spherical singlet elements are often required to collimate the light from a laser diode. A single aspheric lens can collimate the highly divergent emission of a laser diode without introducing spherical aberration, when used as shown in Figure 6.

Fiber Coupling

When coupling light into a fiber, it is often necessary to focus a collimated beam of light to a diffraction-limited spot. Typically, single spherical elements and achromatic doublets are not capable of achieving such a small spot size; spherical aberration is the limiting factor rather than diffraction. Since aspheric lenses are designed to eliminate spherical aberration, only diffraction limits the size of the focal spot.


Lens Material Selection

Thorlabs' lenses are manufactured using a variety of optical materials. The table below should aid with the selection of a lens best suited for use at a particular wavelength. To view transmission vs. wavelength plots for either the uncoated material or the material with an appropriate coating, please click on the appropriate icon below.

MaterialDescriptionTransmission PlotsTransmission Plots with Coatings
N-BK7 N-BK7 has transmission from 350 nm to 2.0 µm. N-BK7 is probably the most common optical glass used for high quality optical components. Transmission  -
UV Fused Silica (UVFS) UV-grade fused silica offers high transmission in the deep UV and extremely low fluorescence levels compared to natural quartz, making it an ideal choice for applications from the UV to the near IR. In addition, UV fused silica has better homogeneity and a lower coefficient of thermal expansion than BK7. UVFS transmission ranges from 185 nm to 2.1 µm. Transmission Transmission
N-SF11 N-SF11 has a transmission ranging from 420 nm to 2.3 µm. Since the Abbe Number of N-SF11 (25.76) is lower than that for N-BK7 (64.17), lenses fabricated from N-SF11 will exhibit higher dispersion than those fabricated from N-BK7. Transmission  -
Calcium Fluoride (CaF2) CaF2 is commonly used for applications requiring high transmission in the infrared and ultraviolet spectral ranges. Its extremely high laser damage threshold makes it useful for use with excimer lasers. Transmission from 180 nm to 8 µm. Transmission Transmission
Barium Fluoride (BaF2) Barium Fluoride is transparent from the UV to the IR. The material is less resistant to water than CaF2. The material is relatively hard, but very sensitive to thermal shock. Of the Typical fluorides it is the most resistant to high energy radiation.  - Transmission
Silicon
(Si)
Silicon Plano-Convex lenses are an idal choice for applications from 1.2 - 8 µm and are particularly well suited for imaging, biomedical, and military applications.  - Transmission
Zinc Selenide (ZnSe) With a transmission range from 600 nm - 16 µm, zinc selenide Plano-Convex lenses are ideal for IR applications. Due to the low absorption coefficient, these lenses are also particularly well suited for high-power CO2 laser applications. In contrast to Ge and Si, which also transmit in this spectral range, ZnSe transmits some visible light, thereby allowing for visual alignment of the optic. Transmission
Germanium (Ge) The transmission characteristics of germanium in the IR region of the spectrum makes it an ideal choice for imaging 2.0 -2.6 µm light. Germanium Plano-Convex lenses are particularly well suited for biomedical and military imaging applications.  - Transmission
Magnesium Fluoride (MgF2) Magnesium Fluoride, an extremely rugged and durable material, is transparent over an extensive range of wavelengths from the UV to the IR. Transmission  -
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