1. General Discussion

2. Combination of Errors and Total Error

3. Analysis of Power and Energy Calibration Errors

4. Detailed Analysis of Power and Energy Calibration Errors

**1. General Discussion**

This document discusses the interpretation and basis for stated measurement accuracy of Ophir Laser Power/Energy meters.

The total accuracy of measurement of a laser power/energy meter is affected by the following factors:

1. The calibration accuracy of the measuring head at the power level, energy level and wavelength at which it was calibrated.

2. The energy calibration error, i.e. the extra error that is due to the extra calibration step necessary to calibrate energy. This is of concern only for thermal heads

3. The wavelength dependence of the head, i.e. if it was calibrated at one wavelength and the measurement is with a laser of a different wavelength, how much this affects the accuracy of the measurement.

4. The linearity of the head, i.e. if we increase the input power or energy by a factor of say 2, do we get twice the reading.

5. The uniformity of reading over the surface, i.e. if the head is calibrated with a small laser beam in the center of the absorber, how much will this change if the beam is not centered or is large sized?

6. The pulse rate dependence in the case of pyroelectric heads, i.e. how much does the reading vary depending on what is the pulse rate of the laser.

7. The calibration accuracy of the display unit.

Before focusing on (1) and (2), the primary subject of this document, we will go over the other factors in measurement accuracy. **Wavelength:** All absorbers used in power/energy measurement are not entirely flat spectrally, that is, they vary in absorption with wavelength. For this reason, Ophir measuring heads are usually calibrated at more than one wavelength. If the absorption changes only slightly with wavelength, then we define wavelength regions such as <600nm, >600nm and give a calibration within these regions. In that case, the error in measurement between the wavelength the device was calibrated for and the measurement wavelength is assumed to be within the primary wavelength calibration error. If the absorption difference between the nearest calibration wavelength and the measurement wavelength is larger than 1-2%, then either we add to the specification an error with wavelength in that region or calibrate over a continuous calibration curve covering all wavelengths in the region. **Linearity:** The linearity of Ophir heads is always given in the published specification for thermal and pyroelectric heads and the expected error due to nonlinearity is to be added to the basic calibration error as discussed below. Note that for thermal heads, the linearity error is in general +/-1% or whatever is in the specification for that particular head. For photodiode heads, the linearity error is not published but it is always less than ±1% except very close to maximum power. If the power level is less than 70% of maximum power for photodiode heads, then the linearity will be within ±0.5%. **Uniformity:** The uniformity of Ophir heads is in general not given in the specification but in most cases it is ±2% maximum variation for beam position anywhere within the central 80% of the area of the aperture for thermal and photodiode heads. For pyroelectric heads the uniformity error is generally less, on the order of ±1%. Since Ophir heads are always calibrated with the beam centered on the absorber, if the measurement is made with the beam centered and the beam is not larger than 1/4 the aperture, this error can in most cases be ignored. **Pulse Rate and Pulse Width:** Pyroelectric heads have some pulse rate dependence. In general, the pulse rate dependence is low and essentially random for pulse rates less than about 70% of the maximum pulse rate. Near the maximum pulse rate you can expect the error to be near the maximum stated. Ophir design pyroelectric heads have almost no pulse width dependence so this can be ignored. **Display:** As can be seen below, in general, the error of calibration of the display is much smaller than the calibration error of the measuring head (~0.3%) and therefore can be ignored in most cases in the combination of errors. **2. Combination of Errors and Total Error**

Ophir published calibration errors are in general 2 Sigma or K=2 error. That means that statistically, in 95% of cases, the error of the system measured will not exceed the stated error. For example, if the stated error is ±3%, then in 95% of the cases, the error will not exceed 3% and in 99% of the cases will not exceed 4%. The total expected error will be in the worst case, the sum of the various contributing errors.

If you are working at <70% of maximum power or pulse rate, the linearity error can be assumed to be random and if the beam is not larger than 1/4 the aperture and is centered, the uniformity error can be ignored. In that case you may use statistical combination of errors to compute expected total error. For instance if the stated linearity is ±1%, the stated pulse rate dependence is ±1% and the stated calibration error is ±3% then the 2 sigma total error can be taken to be √ (0.03)² + (0.01)² + (0.01)² = 3.3%. If the pulse rate or power approaches the maximum permitted, then you must take the maximum value as the expected total error i.e. 0.03 + 0.01 + 0.01 = 5% in the above example. Since the display error is so low, it can be ignored in most cases. **3. Analysis of Power and Energy Calibration Errors** **Thermal and RP heads**

Ophir measurement heads are calibrated first for power by substituting the head under calibration for the reference master head while holding the laser average power constant. The heads are usually calibrated at two or three specified wavelengths.

At each wavelength, the sensitivity is measured at two or three powers and the sensitivity used for calibration is the average of the measured sensitivities. If the sensitivity varies more than the specified linearity limits, the head is disqualified.

The variation in absorption between wavelengths is not ordinarily more than ±2% within a wavelength region and therefore the user can usually just choose the power meter wavelength closest to his wavelength. For interpolation, the user can refer to spectral curves in the Ophir catalog.

Single shot energy is calibrated after the head is calibrated for power by first measuring the laser power on the head, then passing the same power through a calibrated shutter and adjusting the reading to equal energy = power x time.

The RP type head does not need separate calibration for rapid pulse energy since we rely on the high linearity of the photodiodes and the high (1 in 104) accuracy of the pulse rate measurement so the energy accuracy will not significantly vary from the power accuracy. This is true as long as the following conditions apply:

a. The photodiodes are not significantly saturated. If there is saturation, the error in reading will be as follows:

error % = (% saturation) x [1- (energy of reading)/(average energy)]

Thus the error will not be large unless the photodiode is both saturated and there is a large pulse to pulse variation in energy.

The RP head is designed and tested in such a fashion that there is not more than 20% saturation at the highest energy of any given scale and usually much less.

b. There is not a large spatial variation in beam intensity profile from pulse to pulse. Slow variations, (<< thermal response time) are permitted. **4. Detailed Analysis of Power and Energy Calibration Errors**

We now analyze how we arrive at the basic power and energy calibration errors as stated in our specification sheets. **Power and Energy Calibration Error Estimation (heads for powers <300W)**

We use statistical combination of errors to estimate the various sources of calibration error and the total expected error from the various contributions.

Item | Explanation | ||
---|---|---|---|

1 | Variation from one NIST calibration to the next | ±1.0% | From statistics of error of heads send for NIST calibration |

2 | Transfer of calibration from NIST master to working master | ±0.3% | From statistics of deviations between calibration and independent check of calibration for this special calibration |

3 | Transfer of power calibration from working master to head under calibration | ±0.5% | From statistics of deviations between calibration and independent check of calibration |

Combined power calibration error | ±1.2% | From RMS combination of errors | |

Total power calibration error |
±2.3% |
95% of cases are within 2.0 std deviations | |

4 | Additional error in calibration of single shot energy | ±1.5% | From statistics of deviations between calibration and independent check of calibration as well as estimated systematic errors |

Combined energy calibration error | ±1.9% | From RMS combination of errors | |

Total energy calibration errorExpanded error K=2.0 (95% confidence level) |
±3.8% |
95% of cases are within 2.0 std deviations |

The above analysis applies for the wavelength and power at which the calibration was done. If the user measures at different wavelengths or powers, additional maximum errors apply as described above in section 1 and 2. **Pyroelectric heads**

Ophir pyroelectric heads are calibrated for energy by substituting the head under calibration with the reference master head while holding the laser average power constant. The heads are usually calibrated at two or three specified wavelengths. The master head is a thermal power measuring head and is measuring average power while the laser is held to an exact repetition pulse rate, usually 10Hz. **Error Estimation **

Item | Explanation | ||
---|---|---|---|

1 | Variation from one NIST calibration to the next | ±0.4% | From statistics of error of heads send for NIST calibration |

2 | Transfer of calibration from NIST master to working master | ±0.6% | From statistics of deviations between calibration and independent check of calibration for this special calibration |

3 | Transfer of calibration from working master to head under calibration | ±1.0% | From statistics of deviations between calibration and independent check of calibration |

Combined calibration error | ±1.2% | From RMS combination of errors | |

Total energy calibration error Expanded error K=2.0 (95% confidence level) |
±2.5% |
95% of cases are within 2.0 std deviations |

If the user measures at different energy levels than the calibration energy level, the maximum error is the published linearity limit, usually ±2% This linearity is determined by varying the energy at a given pulse rate and measuring the output versus an average power reading on a precision thermal head.

The head is calibrated exactly at selected wavelengths. The variation in absorption between wavelengths for the BB (broadband) type heads is not ordinarily more than ±5% and therefore the user can usually just choose the power meter wavelength closest to his wavelength If the user measures at wavelengths different from the calibration wavelengths, add the additional errors in the table given in the Ophir catalog for the particular type of head.

The metallic absorber heads have a larger variation in absorption over the wavelength range (as much as 50%) and therefore the head has stored in it a wavelength curve which has been determined both by spectrophotometer measurements and by measurements at various laser wavelengths. For each head, this curve is corrected at two or three points and the calibration curve is then “stretched” to fit the test wavelengths, changing the intervening wavelengths proportionately. The Ophir catalog gives the estimated maximum additional error in calibration for measurement at various wavelengths.

To get the total expected error, you must combine the calibration, linearity, wavelength and pulse rate errors as described in section 2 above. **Photodiode heads**

Ophir photodiode heads are calibrated first for power by running an automated spectral scan of the NIST traceable head at intervals of 5nm over the spectral range then a scan of the head under calibration for the same spectral range. The head scan is done twice, with filter out and filter in. The head is then calibrated automatically by the data thus gathered. Note that the light source is stabilized and does not significantly change intensity between scans.

After the above process, the calibrated head is checked against the master at several individual wavelengths of a laser or spectral lamp source. The wavelengths include points near the center of the spectrum, near the edges of the spectrum and points in between. If the discrepancy between the master and head is more than twice the specified calibration accuracy of the head at that wavelength, the calibration is disqualified.

The calibration curve is then “stretched” to fit the test wavelengths, changing the intervening wavelengths proportionately.

Photodiode heads have a uniformity of ±2% over 80% of the aperture.

Since photodiode heads are very linear and are calibrated continuously over the entire spectrum, the total error can in general to be taken as the calibration error without adding any additional errors as long as the beam is well centered on the detector. **Error Estimation (for filter out and filter in setting )**

Item | Wavelength range | Explanation | |||
---|---|---|---|---|---|

200-400nm | 400-950nm | >950nm | |||

1 | NIST RMS error | ±0.2% | ±0.8% | ±1.1% | From RMS errors in calibration as stated by NIST in calibration report |

2 | Transfer of calibration from NIST master to working master | ±1.5% | ±0.4% | ±0.7% | From statistics of deviations between calibration and independent check of calibration for this special calibration |

3 | Transfer of power calibration from working master to head under calibration (filter out) | ±1.5% | ±0.4% | ±0.7% | From statistics of deviations between calibration and independent check of calibration. Long wavelength variation includes temp variations |

Transfer of power calibration from working master to head under calibration (filter in) | ±4.8% | ±1.2% | ±1.9% | ||

5 | Combined power calibration error –filter out | ±2.4% | ±1.2% | ±1.5% | From RMS combination of errors |

Filter in | ±5.0 | ±1.5% | ±2.3% | ||

6 | Total power cal errorExpanded error K=2.0 (95% confidence level) filter out |
±4.8% |
±2.4% |
±3.0% |
95% of cases are within 2.0 std deviations |

Filter in | ±10.0% |
±3.0% |
±4.6% |

**Displays**

Ophir displays are calibrated with an automated calibration unit which consists of a precision voltage source and a set of switchable precision resistors. This unit injects known currents into the display under calibration in an automated system. The reading of the display is compared to the known current and appropriate correction factors are stored in the display so that the reading will be the same as the known current. This is done for all 16 ranges of the display, where the zero offset is measured and compensated for in each range. At final QC, the calibrated display is tested against a different calibration unit and it must pass on all ranges within the specified limits.

The calibration unit itself is calibrated periodically against a precision Fluke volt-ohm meter that is periodically calibrated by the local Standards Institute. **Error Estimation for Display Calibration**

Item | Explanation | ||
---|---|---|---|

1 | Variation from one calibration of calibration unit to the next calibration | ±0.033% | From statistics of error of calibration check by Standards Institute periodic test. This includes uncertainty of Standards Institute calibration itself. |

2 | Transfer of calibration from calibration unit to display | ±0.2% | From worst case permissible error on final QC test on calibrated unit at 100% confidence level. |

Total display calibration error Expanded error K=2.5 (>99% confidence level) |
±0.3% |
>99% of cases are within 2.5 std deviations |

Revision 13 4 March 2009