---
title: "Jones Matrix (Polarizer + Waveplate) calculator — AperiOptic"
description: "Output intensity after polarizer at α then waveplate (retardance δ, axis β). Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/jones-matrix-polarizer-waveplate"
---

# Jones Matrix (Polarizer + Waveplate) calculator

Output intensity after polarizer at α then waveplate (retardance δ, axis β).

Category: [Polarization](https://aperioptic.com/calculators)

Formula: `E_out = W(δ,β) · P(α) · E_in`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Polarizer α | `alpha` | deg | 0 |
| Retardance δ | `delta` | deg | 90 |
| WP axis β | `beta` | deg | 45 |

## Result with the default inputs

- |Ex|: 0.7071
- |Ey|: 0.7071
- Intensity: 1

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/jones-matrix-polarizer-waveplate?alpha=0`](https://aperioptic.com/calculators/jones-matrix-polarizer-waveplate?alpha=0). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Jones calculus](https://en.wikipedia.org/wiki/Jones_calculus)

[All optics calculators](https://aperioptic.com/calculators)

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The interactive page: https://aperioptic.com/calculators/jones-matrix-polarizer-waveplate (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt