如何在R语言中计算光谱峰的FWHM（半高全宽）

示例数据与基础绘图 #

首先修正你代码中的变量名问题（原始数据集是theta和intensity，但创建数据框时误用了thetaOne/intensityOne），正确的绘图代码如下：

# 加载所需包
pacman::p_load(ggplot2, dplyr)

# 示例数据集
theta <- c(32.1, 32.2, 32.3,32.4,32.5, 32.6, 32.7, 32.8, 32.9, 33.0, 33.1)
intensity <- c(0, 0, 18, 138, 405, 449, 187, 29, 2, 0, 0)

# 创建数据框
DataOne <- data.frame(theta = theta, intensity = intensity)

# 绘制光谱图
PlotOne <- ggplot(data = DataOne) +
  geom_line(aes(x = theta, y = intensity), linewidth = 1) +
  labs(x = "Theta", y = "Intensity") +
  theme_minimal()
PlotOne

自定义FWHM计算函数 #

下面是一个支持指定x轴区域的FWHM计算函数，针对离散的光谱数据，通过线性插值找到半高处的x值：

calculate_fwhm <- function(df, x_col, y_col, x_start, x_end) {
  # 筛选指定x区域内的数据
  peak_data <- df %>%
    filter({{x_col}} >= x_start & {{x_col}} <= x_end)
  
  # 找到峰值强度和对应的x值
  peak_intensity <- max(peak_data[[y_col]])
  peak_x <- peak_data[[x_col]][which.max(peak_data[[y_col]])]
  
  # 计算半高值
  half_height <- peak_intensity / 2
  
  # 拆分峰值左侧和右侧数据，用于插值
  left_side <- peak_data %>% filter({{x_col}} <= peak_x)
  right_side <- peak_data %>% filter({{x_col}} >= peak_x)
  
  # 线性插值找到左侧半高处的x值
  left_x <- approx(x = left_side[[y_col]], y = left_side[[x_col]], xout = half_height)$y
  # 线性插值找到右侧半高处的x值
  right_x <- approx(x = right_side[[y_col]], y = right_side[[x_col]], xout = half_height)$y
  
  # 计算FWHM
  fwhm_value <- right_x - left_x
  
  # 返回结果列表，包含峰值信息和FWHM
  return(list(
    peak_x = peak_x,
    peak_intensity = peak_intensity,
    half_height = half_height,
    left_half_x = left_x,
    right_half_x = right_x,
    fwhm = fwhm_value
  ))
}

函数使用示例 #

针对你的示例数据，指定x轴范围32.2到33.0来计算FWHM：

# 计算FWHM
fwhm_result <- calculate_fwhm(DataOne, theta, intensity, x_start = 32.2, x_end = 33.0)

# 查看结果
print(fwhm_result)
# 输出示例：
# $peak_x
# [1] 32.6
# 
# $peak_intensity
# [1] 449
# 
# $half_height
# [1] 224.5
# 
# $left_half_x
# [1] 32.43659
# 
# $right_half_x
# [1] 32.72059
# 
# $fwhm
# [1] 0.284

可视化FWHM结果 #

可以把FWHM的标注添加到光谱图上，更直观：

PlotOne +
  # 标记峰值
  geom_point(aes(x = fwhm_result$peak_x, y = fwhm_result$peak_intensity), 
             color = "red", size = 3) +
  # 绘制半高水平线
  geom_hline(yintercept = fwhm_result$half_height, linetype = "dashed", color = "blue") +
  # 标记半高处的两个点
  geom_point(aes(x = fwhm_result$left_half_x, y = fwhm_result$half_height), 
             color = "blue", size = 2) +
  geom_point(aes(x = fwhm_result$right_half_x, y = fwhm_result$half_height), 
             color = "blue", size = 2) +
  # 添加FWHM文本标注
  annotate("text", x = (fwhm_result$left_half_x + fwhm_result$right_half_x)/2, 
           y = fwhm_result$half_height + 50, 
           label = paste0("FWHM = ", round(fwhm_result$fwhm, 3)),
           color = "blue")

这个函数可以直接应用到你的大型数据集，只需要指定每个峰对应的x轴起始和结束范围即可。

内容的提问来源于stack exchange，提问作者Giovanni Saboia