# Laser NOHD and Eyewear Optical Density Calculator

> Source: https://netray.co/tools/laser-nohd-eyewear-optical-density-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Calculate nominal ocular hazard distance and the optical density needed at a given distance for a continuous-wave laser, from power, beam size, divergence and MPE.

## Category

ehs-workforce

## Industry

Photonics and Optics Manufacturing

## Audience

- Laser safety officer
- EHS manager
- Photonics production supervisor

## Tool

**Kind:** calculator

**Inputs:**

#### CW laser power

**Key:** p

**Type:** number

**Default:** 5

**Min:** 0

**Step:** 0.1

**Unit:** W

#### Beam diameter at aperture

**Key:** a

**Type:** number

**Default:** 4

**Min:** 0.1

**Step:** 0.1

**Unit:** mm

#### Full-angle beam divergence

**Key:** div

**Type:** number

**Default:** 1

**Min:** 0.01

**Step:** 0.05

**Unit:** mrad

#### MPE (irradiance)

**Key:** mpe

**Type:** number

**Default:** 25.4

**Min:** 0.0001

**Step:** 0.1

**Unit:** W/m2

**Help:** Look up the MPE for your wavelength and exposure time in ANSI Z136.1 or IEC 60825-1. 25.4 W/m2 is the visible 0.25 s blink-response value.

#### Viewing distance

**Key:** r

**Type:** slider

**Default:** 10

**Min:** 0

**Max:** 200

**Step:** 1

**Unit:** m

**Outputs:**

#### NOHD

**Key:** nohd

**Expr:** max(0, (1 / (div / 1000)) * (sqrt(4 * p / (pi * mpe)) - a / 1000))

**Format:** decimal

**Primary:** true

**Description:** Meters beyond which unprotected intrabeam viewing is within MPE.

#### Irradiance at aperture

**Key:** e0

**Expr:** 4 * p / (pi * pow(a / 1000, 2))

**Format:** decimal

**Description:** W/m2.

#### Irradiance at viewing distance

**Key:** e_r

**Expr:** 4 * p / (pi * pow(a / 1000 + div / 1000 * r, 2))

**Format:** decimal

**Description:** W/m2 at distance r.

#### Required OD at aperture

**Key:** od0

**Expr:** max(0, log10(e0 / mpe))

**Format:** decimal

**Description:** Eyewear optical density needed at the aperture.

#### Required OD at viewing distance

**Key:** od_r

**Expr:** max(0, log10(e_r / mpe))

**Format:** decimal

**Primary:** true

**Chart:**

#### Required eyewear OD vs viewing distance (m)

**Type:** line

**X:** r

**From:** 0

**To:** 200

**Steps:** 40

**Series:**

- od_r

**Disclaimer:** Screening estimate only for a CW beam with small-angle geometry and no focusing optics. Final hazard evaluation, MPE and eyewear selection must be made by the Laser Safety Officer under ANSI Z136.1, IEC 60825-1 or EN 207 and EN 208.

## Content

**Intro:** The nominal ocular hazard distance tells you how far from a laser an unprotected eye can be exposed within the maximum permissible exposure. This tool computes it, plus the eyewear optical density needed at the aperture and at a chosen distance.

**Sections:**

#### How to use the calculator

**Body:** Enter the laser output power, the beam diameter at the exit aperture, the full-angle divergence and the MPE for your wavelength and exposure duration. Then set the viewing distance. The result gives the NOHD in meters, the irradiance at the aperture and at the distance, and the optical density that eyewear needs to bring that exposure down to the MPE. The sweep shows how required OD falls with distance. Your Laser Safety Officer should confirm all inputs.

**Bullets:**

- Use full-angle divergence in mrad, as datasheets quote it.
- Look up the MPE for the specific wavelength and exposure time.
- Add margin: eyewear should carry a rated OD above the calculated figure.

#### The formulas

**Body:** Irradiance of a diverging beam is E = 4P / (pi (a + theta r)^2), where a is the aperture beam diameter, theta the full-angle divergence in radians and r the distance. Setting E equal to the MPE and solving gives NOHD = (1 / theta)(sqrt(4P / (pi MPE)) - a). Required optical density is OD = log10(E / MPE). A value of 3 means the filter transmits one thousandth of the incident radiation.

#### Worked example

**Body:** A 5 W visible CW laser with a 4 mm beam and 1 mrad divergence has an aperture irradiance near 400,000 W/m2. Against an MPE of 25.4 W/m2 the eyewear OD at the aperture is about 4.2. The NOHD is roughly 500 m, so at 10 m the irradiance is still far above MPE and an OD of 3.1 or more is needed. This shows why even moderate power lasers need beam enclosures and engineering controls, with eyewear as a last layer.

#### Common mistakes

**Body:** Applying a CW formula to a pulsed laser underestimates the hazard, because MPE for pulses uses energy per pulse and different time bases. Another is ignoring specular reflections and focusing optics, which can raise irradiance well beyond the diverging beam model. Using the wrong wavelength band for the MPE, or forgetting that eyewear OD is specific to wavelength, is also frequent. This tool does not replace a documented hazard evaluation and training records.

**Cta:** Netray can help connect laser safety records, eyewear inspections and training status to your ERP so compliance questions are answered from one place.

**Faq:**

#### What is NOHD?

**Answer:** Nominal ocular hazard distance is the distance from the laser along the beam beyond which the irradiance or radiant exposure falls below the maximum permissible exposure for the eye. Within it, direct viewing may exceed safe limits.

#### Which MPE should I use?

**Answer:** The one for your wavelength and exposure duration in ANSI Z136.1 or IEC 60825-1. For visible light, 0.25 s is the aversion-response time, and many safety officers use it. Invisible wavelengths use different durations.

#### Does this work for pulsed lasers?

**Answer:** No. Pulsed lasers use MPE expressed in radiant exposure and require pulse width, repetition rate and multiple-pulse corrections. Consult your laser safety officer or the standard for those cases.

#### Is the OD result the eyewear label?

**Answer:** It is a required minimum. Labels per EN 207 or ANSI show OD and wavelength range with a scale number. Choose eyewear whose rating at your wavelength and exposure mode meets or exceeds the calculated value.

## Search terms

nohd calculator, nominal ocular hazard distance, laser safety eyewear optical density, laser od calculator, maximum permissible exposure calculator, laser safety distance calculation, ansi z136.1 nohd, laser eyewear od formula

---
Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json