Features

• Material: N-BK7
• Wavelength Range: 350 - 2000 nm (Uncoated)
• Available Sizes: Ø6.0 mm, Ø9.0 mm, Ø1/2", Ø1", and Ø2"
• Focal Lengths Available from 10.0 mm to 1.0 m
• Well Suited for Many Finite Imaging Applications
• Offers Excellent Transmittance Throughout the Visible and Near Infrared

Thorlabs' uncoated N-BK7 Bi-Convex Lenses are popular for many finite imaging applications. This type of lens is best suited for use in situations where the object and image are on opposite sides of the lens and the ratio of the image and object distances (conjugate ratio) is between 0.2 and 5. These lenses are designed to have a focal length of f= (R1*R2)/((n-1)*(R2-R1)).

N-BK7 is probably the most common optical glass used for high-quality optical components. It is typically chosen whenever the additional benefits of UV fused silica (i.e., good transmission further into the UV and a lower coefficient of thermal expansion) are not necessary.

Although this page features our uncoated bi-convex lenses, these lenses are also available with one of three antireflection coatings (-A, -B, or -C) deposited on both sides to reduce the amount of light reflected from each surface. Links to each of these pages can be found in the table to the right. Please see the Graphs tab for coating details.

Lens kits are available. Please click here for information.

Zemax Files
Click on the red Document icon next to the item numbers below to access the Zemax file download. Our entire Zemax Catalog is also available.

Below is the transmission curve for N-BK7, a RoHS-compliant form of BK7. Total Transmission is shown for a 10 mm thick, uncoated sample and includes surface reflections. Each N-BK7 bi-convex lenses can be ordered uncoated (available below) or with one of the following broadband AR coatings: 350 - 700 nm (designated with -A), 650 - 1050 nm (designated as -B), or 1050 - 1700 nm (designated as -C).

Our high-performance multilayer AR coatings have an average reflectance of less than 0.5% (per surface) across the specified wavelength ranges and provide good performance for angles of incidence (AOI) between 0° and 30° (0.5 NA). For optics intended to be used at large incident angles, consider using a custom coating optimized at a 45° angle of incidence; this custom coating is effective from 25° to 52°. The plot shown below indicates the performance of the standard coatings in this family as a function of wavelength. Broadband coatings have a typical absorption of 0.25%, which is not shown in the reflectivity plots.

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Click Here for Raw Data

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A Thorlabs technician measuring the irregularity of one of our singlets using a Zygo GPI-XP/D Interferometer.

Introduction
Thorlabs has a series of quality control procedures in order to ensure our singlets meet our standards and specifications. This starts with in-process inspections of the lens’ imaging capabilities and ends with a final inspection of surface quality and dimensions. Specifications for particular products can be found in their linked documentation by clicking the  symbol. This tab will take you through the general process used to check for quality.

Singlet Quality Practices
In-process inspection begins once the singlet has been shaped to specifications. Focal length, surface irregularity, and surface power are checked, following sampling plan Level VI given in MIL-PRF-13830B (see below). These three specifications are imperative for proper imaging. Surface irregularity of parts is kept to below either a quarter wavelength or a half wavelength at 633 nm, depending on the material of the singlet. Below is a graph of over 200 batches of singlets with irregularity data of both their front and back sides.

At this point, some uncoated singlets will proceed to final inspection, while others will receive an antireflective (AR) coating. The application of optical coatings has its own in-process inspections. To ensure the AR coating is applied properly, we verify both reflectance and transmission performance by scanning witness pieces using spectrophotometry; the material of these 2 mm thick witness samples matches the other parts in the run. For reflectance verification, we use at least one witness sample for each coating run. Transmitting optics receive two AR coatings, one on each surface, so for the verification of transmission, we use one witness sample that is also coated on both of its sides. Large runs use multiple witness samples to ensure the uniformity across the deposition chamber. By testing coating performance during every run, variance over time is kept low. To see how coatings vary, see the table below.

Final inspection of both uncoated and AR-coated singlets includes a batch check of diameter and thickness and a 100% visual check to ensure that the surface quality, chamfer, and clear aperture meet our published specifications. While surface quality is cosmetic to a degree, scratches, digs, and other inclusions in the surface of a part can increase the chances of damage to the singlet when used with high-power sources. These inspections are done in a clean, dark room under lighting that meets the requirements of MIL-PRF-13830B. Inspection under a single light source in a dark room allows for inconsistencies in the glass to be located without being obscured by glare or reflections.

MIL-PRF-13830B: Performance Specifications for Optical Components
MIL-PRF-13830B is a document created by the U.S. Army Armament Research, Development and Engineering Center's Defense Quality and Standardization Office for the specifications covering how finished optical components should be manufactured, assembled, and inspected. While primarily for use in letting the military dictate how products they use can be incorporated into their equipment, these standards have been adopted by many optics manufacturers. To download a copy of the full document, click here.

	-A Coating 350 nm to 700 nm	-B Coating 650 nm to 1050 nm	-C Coating 1050 nm to 1700 nm		Singlet Irregularity
Coating Variance: Transmission	Click to Enlarge	Click to Enlarge	Click to Enlarge		Click to Enlarge
Coating Variance: Reflectance	Click to Enlarge	Click to Enlarge	Click to Enlarge

Disclaimer: The coated transmission data presented here are of 2 mm thick witness samples of N-BK7 or equivalent glass, and all the data here are typical. Some variations in performance data will occur from lot to lot. Please contact Technical Support with any questions regarding the use or reliability of these data.

The focal length of a thick spherical lens can be calculated using the thick lens equation below. In this expression, n_l  is the index of refraction of the lens, R₁ and R₂ are the radii of curvature for surfaces 1 and 2, respectively, and d is the center thickness of the lens.

For bi-convex lenses, where the front and back radii of curvature are equal in magnitude and opposite in sign, R₁ = -R₂ = R, we have

The focal length of the lens calculated using the simplified thick lens equation directly above is the distance between the second (back) principle plane (H") and the position at which a collimated beam incident on the curved surface of the bi-convex is focused. The same analysis can be performed using a point source and the first (front) principle plane (H'). The principle plane positions of a thick lens can be calculated with the following equations:

and

Again, for the same bi-convex lens, R₁ = -R₂ = R, we can solve for H' and H' :