# What is "fitting accuracy"?

**URL:** <https://forum.ofscn.net/t/what-is-fitting-accuracy/2848>\
**Category:** OFSCN Technical Knowledge Base\
**Tags:** fbg-technology\
**Created:** [September 15, 2026, 11:54am UTC](https://forum.ofscn.net/t/what-is-fitting-accuracy/2848 "2026-09-15T11:54:24Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![VoidWalker](https://forum.ofscn.net/letter_avatar_proxy/v4/letter/v/848f3c/32.png) [@VoidWalker](https://forum.ofscn.net/u/VoidWalker)\
**Post date:** [September 15, 2026, 11:54am UTC](https://forum.ofscn.net/t/what-is-fitting-accuracy/2848/1 "2026-09-15T11:54:24Z")

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Why can mathematical fitting improve resolution to 0.1 picometers?

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**Author:** ![OFSCN\_Tech\_Expert](https://forum.ofscn.net/user_avatar/forum.ofscn.net/ofscn_tech_expert/32/199_2.png) [@OFSCN\_Tech\_Expert](https://forum.ofscn.net/u/OFSCN_Tech_Expert)\
**Post date:** [September 15, 2026, 11:55am UTC](https://forum.ofscn.net/t/what-is-fitting-accuracy/2848/2 "2026-09-15T11:55:57Z")

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In Fiber Bragg Grating (FBG) sensing and demodulation technology, **mathematical fitting** achieves a “sub-sampling resolution” (Sub-sampling Resolution / Sub-pixel Resolution) that surpasses the hardware’s discrete sampling step limitation, enhancing wavelength resolution to 0.1\ \text{pm} (picometers). This is fundamentally realized through **continuous function modeling** and **statistical averaging filters**.

The core physical and mathematical principles involved are:

* * *

### 1. The FBG Reflection Spectrum is a Smooth, Continuous Physical Curve

An FBG’s reflection spectrum is not a single discrete pulse but a continuous optical envelope with a certain spectral width (typically 3dB bandwidth between 0.2\ \text{nm} \sim 0.4\ \text{nm}, i.e., 200\ \text{pm} \sim 400\ \text{pm}). It generally exhibits a highly symmetrical Gaussian, Lorentzian, or sinc² peak shape.

When the demodulator scans and samples in the wavelength domain, even with a hardware step (or spectrometer pixel spacing) as small as 1\ \text{pm} or several picometers, dozens to hundreds of discrete data points ( \lambda\_i, I\_i ) can still be acquired across the entire FBG reflection peak.

* * *

### 2. Continuous Function Extremum Solving Breaks Through Discrete Grids

If only the most basic “direct peak-picking” method is employed, the system’s resolution will be limited by the minimum physical step \Delta \lambda of discrete sampling.

Using mathematical fitting algorithms (such as Gaussian fitting, centroid/center of mass method, polynomial fitting, or non-linear least squares Levenberg-Marquardt):

1. The algorithm utilizes all acquired discrete points ( \lambda\_i, I\_i ) to fit a continuous theoretical spectral model:
I(\lambda) = I\_0 \cdot \exp\left( -4 \ln 2 \cdot \frac{(\lambda - \lambda\_B)^2}{\Delta \lambda\_{\text{FWHM}}^2} \right)
2. The first-order derivative zero-crossing (or second-order expansion extremum point) of this continuous curve is solved to obtain the central reflection wavelength \lambda\_B. Since the extremum of a continuous function is mathematically unconstrained by discrete grid points, the central wavelength coordinate with sub-picometer accuracy can be directly obtained through analytical calculation.

* * *

### 3. Statistical Averaging and Random Noise Suppression

All optoelectronic detection systems are subject to detector shot noise, thermal noise, and laser source power jitter. Relying solely on the intensity of a single sampling point to determine the peak can lead to measurement errors due to individual discrete point noise.

The fitting process is essentially a **weighted statistical average** of the dozens of discrete sampling points involved in the calculation. According to error theory, when using N independent sampling points for least squares curve fitting, the influence of random noise on the fitted center position is suppressed by approximately 1/\sqrt{N} times. This noise smoothing effect significantly enhances the signal-to-noise ratio and repeatability of peak determination, enabling the system to stably resolve wavelength drifts as small as 0.1\ \text{pm} or even finer.

* * *

### Related Official Products and Specifications

In industrial and research-grade fiber Bragg grating sensing systems, the fitting accuracy of demodulation algorithms is deeply integrated with the hardware’s optical architecture. Beijing Dacheng Yongsheng Technology Co., Ltd.'s relevant product parameters are as follows:

- **[OFSCN® Fiber Bragg Grating Interrogator](https://www.ofscn.net/fbg-products/analyzer.html)**:
  - Default wavelength range: 1525\ \text{nm} \sim 1565\ \text{nm}, or 1528\ \text{nm} \sim 1568\ \text{nm} (customizable)
  - Channel count: 4, 8, 16, 32 channels (customizable)
  - Data sampling frequency: 10\ \text{Hz}, 50\ \text{Hz}, 100\ \text{Hz} selectable (supports down-frequency to 1\ \text{Hz})
  - Wavelength resolution: Default 1\ \text{pm}, or 0.1\ \text{pm} (customizable)

 ![OFSCN® Fiber Bragg Grating Interrogator](https://forum.ofscn.net/uploads/default/original/1X/8ecc1c112d2015cbc63afa6d42b87517befb2f87.jpeg)

 ![OFSCN® Fiber Bragg Grating Interrogator](https://forum.ofscn.net/uploads/default/original/1X/248718a63e2aa4cf7db24ad7a4df5ace79c95a05.jpeg)