R/rapt_recon.R

In aproudian2/rapt: Atom Probe Tomography Analysis

#
# This file contains methods for reconstructing APT data.
#

#### paraOrthoX ####
#' Internal function used by \code{\link{paraOrthoRec}}.
#'
#' @seealso \code{\link{paraOrthoRec}}
paraOrthoX <- function(x, y, a, d) {
  if (x == 0) {
    x <- 1e-12
  }
  x.dat <- (6^(2 / 3) * a^2 * (1 + 2 * a * d) * x^2 * (x^2 + y^2) -
    6^(1 / 3) * (-9 * a^4 * x^3 * (x^2 + y^2)^2 +
      sqrt(3) * sqrt(a^6 * x^6 * (x^2 + y^2)^3 *
        (2 + 12 * a * d + 16 * a^3 * d^3 + 3 * a^2 *
          (8 * d^2 + 9 * (x^2 + y^2)))))^(2 / 3)) /
    (6 * a^2 * (x^2 + y^2) * (-9 * a^4 * x^3 * (x^2 + y^2)^2 +
      sqrt(3) * sqrt(a^6 * x^6 * (x^2 + y^2)^3 *
        (2 + 12 * a * d + 16 * a^3 * d^3 + 3 * a^2 *
          (8 * d^2 + 9 * (x^2 + y^2)))))^(1 / 3))
  return(x.dat)
}
#### paraOrthoY ####
#' Internal function used by \code{\link{paraOrthoRec}}.
#'
#' @seealso \code{\link{paraOrthoRec}}
paraOrthoY <- function(x, y, a, d) {
  if (x == 0) {
    x <- 1e-12
  }
  y.dat <- (y * (6^(2 / 3) * a^2 * (1 + 2 * a * d) * x^2 * (x^2 + y^2) -
    6^(1 / 3) * (-9 * a^4 * x^3 * (x^2 + y^2)^2 +
      sqrt(3) * sqrt(a^6 * x^6 * (x^2 + y^2)^3 *
        (2 + 12 * a * d + 16 * a^3 * d^3 + 3 * a^2 *
          (8 * d^2 + 9 * (x^2 + y^2)))))^(2 / 3))) /
    (6 * a^2 * x * (x^2 + y^2) * (-9 * a^4 * x^3 * (x^2 + y^2)^2 +
      sqrt(3) * sqrt(a^6 * x^6 * (x^2 + y^2)^3 *
        (2 + 12 * a * d + 16 * a^3 * d^3 + 3 * a^2 *
          (8 * d^2 + 9 * (x^2 + y^2)))))^(1 / 3))
  return(y.dat)
}
#### paraOrthoRec ####
#' paraOrthoRec
#'
paraOrthoRec <- function(ato, a, d = 90e7, icf = 1, k = 0) {
  para.x <- apply(ato[, c("dx", "dy")], 1, function(ato) {
    paraOrthoX(ato[1] * 1e8, ato[2] * 1e8, a = a, d = d)
  })
  para.y <- apply(ato[, c("dx", "dy")], 1, function(ato) {
    paraOrthoY(ato[1] * 1e8, ato[2] * 1e8, a = a, d = d)
  })
  para.dat <- data.frame(x = para.x, y = para.y)
  para.dat <- apply(para.dat, 1, function(pos) {
    r <- sqrt(pos[1]^2 + pos[2]^2)
    scale <- icf * (a * r)^k
    new <- scale * pos
    return(new)
  })
  para.dat <- as.data.frame(t(para.dat))
  return(para.dat)
}
#### paraRec ####
#' Reconstruction using a parabolic tip shape assumption.
#'
#' \code{paraRec} creates a reconstruction based upon a parabolic tip shape
#' assumption and parabolic flight paths.
#'
#' @export
paraRec <- function(ato, a, d = 90e7, icf = 1) {
  para.ind <- rownames(ato)
  para.dr <- sqrt(ato[, "dx"]^2 + ato[, "dy"]^2)
  para.dr <- 1e8 * para.dr
  para.theta <- atan2(ato[, "dy"], ato[, "dx"])
  para.fun <- function(r) {
    sqrt((sqrt(16 * a^2 * r^2 + (1 + 4 * a * d)^2) - 4 * a * d - 1) / (8 * a^2))
  }
  para.r <- para.fun(para.dr)
  para.r <- icf * para.r
  para.x <- para.r * cos(para.theta)
  para.y <- para.r * sin(para.theta)
  para.z <- -a * para.r^2
  para.dat <- data.frame(x = para.x, y = para.y, z = para.z)
  rownames(para.dat) <- para.ind
  return(para.dat)
}

#### sphereRec ####
#' Reconstruction using the sphere on cone method
#'
#' \code{sphereRec} creates a reconstruction based on a sphere on post tip
#' shape assumption. A conical post will be implemented in the future.
#'
#' @export
sphereRec <- function(ato, r, d = 90e7, icf = 1) {
  sph.ind <- rownames(ato)
  sph.dr <- sqrt(ato[, "dx"]^2 + ato[, "dy"]^2)
  sph.dr <- 1e8 * sph.dr
  sph.theta <- atan2(ato[, "dy"], ato[, "dx"])
  sph.fun <- function(r, dr, d) {
    x <- dr / d
    r * x / sqrt(x^2 + 1)
  }
  sph.r <- sph.fun(r, sph.dr, d)
  sph.r <- icf * sph.r
  sph.x <- sph.r * cos(sph.theta)
  sph.y <- sph.r * sin(sph.theta)
  sph.z <- sqrt(r^2 - sph.r^2) - r
  sph.dat <- data.frame(x = sph.x, y = sph.y, z = sph.z)
  rownames(sph.dat) <- sph.ind
  return(sph.dat)
}