# Focused Laser Spot Size and Depth of Focus Calculator > Source: https://netray.co/tools/focused-spot-size-depth-of-focus-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Estimate the focused spot diameter and depth of focus of a laser through a lens, and compare against the diffraction-limited Airy disk. ## Category industry-templates ## Industry Photonics and Optics Manufacturing ## Audience - Laser process engineer - Optical designer - Manufacturing engineer ## Tool **Kind:** calculator **Inputs:** #### Wavelength **Key:** lam **Type:** number **Default:** 532 **Min:** 200 **Max:** 12000 **Step:** 1 **Unit:** nm #### Lens focal length **Key:** f **Type:** number **Default:** 100 **Min:** 1 **Step:** 1 **Unit:** mm #### Collimated beam diameter at lens (1/e2) **Key:** d **Type:** slider **Default:** 8 **Min:** 1 **Max:** 30 **Step:** 0.5 **Unit:** mm #### Beam quality M squared **Key:** m2 **Type:** number **Default:** 1.2 **Min:** 1 **Step:** 0.05 **Outputs:** #### f-number (f / D) **Key:** fnum **Expr:** f / d **Format:** decimal #### Approximate numerical aperture **Key:** na **Expr:** d / (2 * f) **Format:** decimal **Description:** Small-angle approximation, D / 2f. #### Focused spot diameter (1/e2) **Key:** spot **Expr:** 4 * m2 * lam * 0.001 * f / (pi * d) **Format:** decimal **Primary:** true **Description:** um, Gaussian beam focus. #### Airy disk diameter (uniform illumination) **Key:** airy **Expr:** 2.44 * lam * 0.001 * f / d **Format:** decimal **Description:** um, diameter to first dark ring. #### Depth of focus (2 x Rayleigh range) **Key:** dof **Expr:** 2 * pi * pow(spot / 2, 2) / (m2 * lam * 0.001) / 1000 **Format:** decimal **Primary:** true **Description:** mm. **Chart:** #### Focused spot diameter (um) vs input beam diameter (mm) **Type:** line **X:** d **From:** 2 **To:** 30 **Steps:** 30 **Series:** - spot **Disclaimer:** Ideal aberration-free lens and Gaussian beam. Spherical aberration and clipping at the lens aperture increase the real spot. ## Content **Intro:** Laser marking, micromachining and fiber alignment all depend on how small a spot you can focus and how tightly the focal plane must be held. This calculator links focal length, input beam size and M squared to the spot and depth of focus. **Sections:** #### How to use the calculator **Body:** Enter the laser wavelength, the lens focal length, the 1/e2 diameter of the collimated beam entering the lens and the M squared of the beam. The spot diameter output is for a Gaussian beam with the standard focusing relation. The Airy disk is shown for comparison and applies to uniform illumination of a circular aperture. The chart sweeps beam diameter to show that a larger beam on the same lens gives a smaller spot, until you hit the lens aperture limit. **Bullets:** - Make the lens clear aperture at least 1.5 to 2 times the 1/e2 beam diameter to avoid clipping. - Shorter focal length also gives smaller spot and a much shorter depth of focus. - Check scan lenses: their quoted spot already includes field flatness limits. #### The formulas **Body:** For a Gaussian beam focused by a lens, the focused spot diameter is 4 M2 lambda f / (pi D), where D is the 1/e2 input diameter. The waist radius is half of that and the Rayleigh range follows as pi w0^2 / (M2 lambda). Depth of focus is taken here as twice the Rayleigh range. The Airy diameter 2.44 lambda f / D describes the first dark ring for a top-hat beam. In a Gaussian beam with no aperture clipping there are no rings. #### Worked example **Body:** A 532 nm laser with M squared of 1.2 and an 8 mm beam through a 100 mm lens focuses to about 10 um diameter, with a depth of focus near 0.3 mm. That means a part height variation of 0.3 mm degrades the spot noticeably. Cutting the beam to 4 mm doubles the spot to about 20 um but quadruples the depth of focus, which is a common trade for processes on non-flat parts. #### Common mistakes **Body:** Using the output diameter of the laser head rather than the actual beam on the lens misses any expander or truncation upstream. Another error is treating the calculated spot as the process feature size: thermal diffusion, threshold effects and material response often make the machined feature larger or smaller than the optical spot. Verify against a burn test or a camera at the work plane, and store the settings with the job routing in your ERP or MES. **Cta:** Netray can help move laser process settings and verification results out of spreadsheets and into your routing and quality records, on-prem if required. **Faq:** #### Why does a larger beam give a smaller spot? **Answer:** Spot diameter scales with wavelength times focal length divided by beam diameter. A wider beam fills more of the lens, which means a higher numerical aperture and a tighter diffraction-limited focus, until the lens aperture or aberrations take over. #### Is the Airy disk or Gaussian spot correct for my laser? **Answer:** Most lasers have near Gaussian beams without hard aperture clipping, so use the Gaussian result. Use the Airy figure for uniformly illuminated apertures, such as a heavily overfilled lens or an imaging system. #### How do I count for lens aberration? **Answer:** Use the calculated spot as a lower bound. Choose lens designs rated as diffraction limited at your wavelength and f-number, such as aspheric singlets or multi-element objectives, and confirm with a beam profiler at the focus. #### What about focal shift with temperature? **Answer:** High-power lenses and protective windows show thermal focal shift. Compare the depth of focus above with your expected shift; if the shift is a significant fraction, plan focus tracking or lower the numerical aperture. ## Search terms focused spot size calculator, laser depth of focus calculator, airy disk diameter calculator, diffraction limited spot size, laser focus spot size formula, f-number numerical aperture calculator, laser marking spot size, focal length beam diameter spot --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json