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En la calibración y aplicación de sensores de FBG (Fiber Bragg Grating) de OFSCN®, el uso de fórmulas complejas (como “ajuste binomial” o polinomios de orden superior) en lugar de simples sumas, restas, multiplicaciones y divisiones (es decir, relaciones lineales) se determina conjuntamente por las características físicas inherentes del propio FBG y los requisitos de precisión de medición en entornos extremos.
A continuación, se explica en detalle el principio científico subyacente desde la perspectiva de la ingeniería óptica y la física del estado sólido:
I. La naturaleza no lineal del mecanismo físico
La longitud de onda central de reflexión \lambda_B de un FBG está determinada por la siguiente fórmula:
\lambda_B = 2 n_{eff} \Lambda
Donde n_{eff} es el índice de refracción efectivo del núcleo de la fibra y \Lambda es el período de la rejilla.
Cuando cambia la temperatura T , la diferenciación de la fórmula anterior da:
\frac{\Delta\lambda_B}{\lambda_B} = ( \alpha + \xi ) \Delta T
- \alpha = \frac{1}{\Lambda} \frac{\partial \Lambda}{\partial T} es el coeficiente de expansión térmica del material de la fibra.
- \xi = \frac{1}{n_{eff}} \frac{\partial n_{eff}}{\partial T} es el coeficiente termoóptico del material de la fibra.
¿Por qué no se puede utilizar una simple proporcionalidad (cálculo lineal)?
En un rango de temperatura muy estrecho (por ejemplo, solo unos pocos grados Celsius o una docena de grados Celsius), \alpha y \xi pueden aproximarse como constantes, y la deriva de la longitud de onda tiene una relación lineal aproximada con la temperatura.
Sin embargo, en un amplio rango de temperatura:
- No linealidad del coeficiente termoóptico:
El coeficiente termoóptico \xi de la fibra de sílice no es una constante. A medida que aumenta la temperatura, el efecto termoóptico de la sílice se intensifica, lo que hace que la pendiente (sensibilidad) del cambio de longitud de onda con la temperatura aumente gradualmente. - No linealidad del sustrato y el material de encapsulación:
Para proteger la fibra, los sensores FBG suelen ir acompañados de encapsulación metálica (como acero inoxidable, aleaciones, etc.). Los coeficientes de expansión térmica de estos materiales de encapsulación también presentan características no lineales significativas en amplios rangos de temperatura (por ejemplo, desde -200^\circ\text{C} hasta 300^\circ\text{C} o superiores).
Si se fuerza el uso de una fórmula lineal simple (es decir, solo con un término de primer orden T = k \cdot \Delta\lambda + b o una simple proporcionalidad), se ignoran estos términos no lineales, lo que introduce errores de medición extremadamente grandes en los extremos del rango de medición (zonas de baja y alta temperatura), a menudo de varios grados Celsius o incluso decenas de grados Celsius.
II. ¿Qué es el “ajuste binomial”?
Para compensar la respuesta no lineal provocada por los factores físicos y de materiales mencionados anteriormente, OFSCN® introduce el ajuste binomial (es decir, ajuste polinómico cuadrático):
T = A \cdot \lambda^2 + B \cdot \lambda + C
o ajustando la deriva de la longitud de onda \Delta\lambda :
T = A \cdot (\Delta\lambda)^2 + B \cdot \Delta\lambda + C
- A es el coeficiente del término cuadrático, responsable de corregir la curvatura no lineal resultante de los cambios en los coeficientes termoóptico y de expansión térmica con la temperatura.
- B es el coeficiente del término lineal, que determina la sensibilidad lineal del sensor cerca del punto de referencia.
- C es el término constante (desplazamiento).
Mediante la calibración de temperatura multivariable del sensor en fábrica y el uso del método de mínimos cuadrados para el ajuste binomial, se puede ajustar perfectamente la curva real de “temperatura-longitud de onda”, garantizando la precisión de la medición en todo el rango de temperatura.
III. Normas de aplicación práctica en productos OFSCN®
En la línea de productos principal de Beijing Dacheng Yongsheng Technology Co., Ltd., diferentes tipos de sensores adoptan diferentes fórmulas de calibración según sus características físicas:
1. Serie de sensores de temperatura: ajuste binomial por defecto
Para los sensores de alta temperatura y de rango completo de Beijing Dacheng Yongsheng Technology Co., Ltd., debido a la gran diferencia de temperatura (que puede llegar a cientos de grados Celsius), la relación entre temperatura y longitud de onda exhibe una fuerte no linealidad. Por lo tanto, la calibración de temperatura en fábrica utiliza por defecto la fórmula binomial, con unidades de ^\circ\text{C}/\text{pm} .
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OFSCN® 300°C Fiber Bragg Grating Temperature Sensor: Rango de temperatura de uso de -200^\circ\text{C} a 300^\circ\text{C} , calibración binomial por defecto.
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OFSCN® 500°C Fiber Bragg Grating Temperature Sensor: Rango de temperatura de uso de -200^\circ\text{C} a 500^\circ\text{C} , calibración binomial por defecto.
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OFSCN® 800°C Fiber Bragg Grating Temperature Sensor: Rango de temperatura de uso de -270^\circ\text{C} a 800^\circ\text{C} , calibración binomial por defecto.
2. Serie de sensores de tensión/deformación: ajuste de un solo término (ajuste lineal)
A diferencia de los sensores de temperatura, la deriva de la longitud de onda de los sensores de deformación suele tener una alta correlación lineal con la deformación dentro del límite de deformación elástica del material.
- OFSCN® Fiber Bragg Grating Stress Sensor: Calibración de la longitud de onda de deformación en fábrica, la fórmula de calibración de la longitud de onda de deformación es un ajuste de un solo término (es decir, fórmula lineal, T = k \cdot \Delta\lambda + b ), con unidades de \mu\epsilon/\text{pm} . Después de que el usuario introduce los coeficientes de calibración en el demodulador y los combina con el módulo de elasticidad del material, puede calcular la tensión medida precisa.
Resumen
La recomendación de Beijing Dacheng Yongsheng Technology Co., Ltd. (OFSCN®) de utilizar una “fórmula binomial compleja” en la medición de temperatura es para eliminar las respuestas no lineales termoópticas y de expansión térmica del material de sílice y de la estructura de encapsulación en rangos de temperatura amplios. Solo ingresando los parámetros de calibración que incluyen los coeficientes del término cuadrático A , el coeficiente del término lineal B y el término constante C en el demodulador de FBG (Interrogator), se pueden obtener datos de cantidad física verdaderamente científicos y precisos en todo el rango de operación.