diff --git a/src/backscattering_analyzer/__init__.py b/src/backscattering_analyzer/__init__.py
index 2a72377..2ee35dc 100644
--- a/src/backscattering_analyzer/__init__.py
+++ b/src/backscattering_analyzer/__init__.py
@@ -7,12 +7,16 @@ install(__name__)
 logger = getLogger(__name__)
 
 
-def show_projection(experiment: "Experiment") -> None:
+def show_projection(
+    experiment: "Experiment",
+    start_frequency: float | None = None,
+    end_frequency: float | None = None,
+) -> None:
     """
     Show projection data with matplotlib
     """
     logger.debug(_("showing experiment result"))
-    from matplotlib.pyplot import loglog, show, legend, close
+    from matplotlib.pyplot import loglog, show, legend, close, vlines
 
     excited = experiment.signals["excited"].psd().sqrt()
     reference = experiment.signals["reference"].psd().sqrt()
@@ -28,6 +32,24 @@ def show_projection(experiment: "Experiment") -> None:
         (experiment.projection + reference).y,
         label="sum reference + excited",
     )  # type: ignore[ReportUnusedCallResult]
+    if start_frequency is not None:
+        vlines(
+            [
+                start_frequency,
+            ],
+            min(experiment.projection.y),
+            max(experiment.projection.y),
+            color = 'k',
+        ) # type: ignore[ReportUnusedCallResult]
+    if end_frequency is not None:
+        vlines(
+            [
+                end_frequency,
+            ],
+            min(experiment.projection.y),
+            max(experiment.projection.y),
+            color = 'k',
+        ) # type: ignore[ReportUnusedCallResult]
     legend()  # type: ignore[ReportUnusedCallResult]
     show()
     close()
diff --git a/src/backscattering_analyzer/experiment.py b/src/backscattering_analyzer/experiment.py
index 799b9f9..f6a7661 100644
--- a/src/backscattering_analyzer/experiment.py
+++ b/src/backscattering_analyzer/experiment.py
@@ -1,7 +1,7 @@
 from pathlib import Path
 from tomllib import load
 
-from numpy import argmin, float64, pi
+from numpy import argmin, float64, pi, log10
 from numpy.core.function_base import logspace
 from numpy.core.multiarray import array
 from numpy.typing import NDArray
@@ -295,9 +295,11 @@ class Experiment:
 
     def fit_factors(
         self,
-        start: float = 15,
-        end: float = 100,
-        x: NDArray[float64] | None = None,
+        scatter_min: float = 1e-20,
+        scatter_max: float = 1,
+        start_frequency: float = 15,
+        end_frequency: float = 100,
+        precision: int = 3,
     ) -> dict[str, float]:
         """
         Find the best factor (first order only) to get the projection
@@ -311,35 +313,51 @@ class Experiment:
             excited,
             reference,
             phase,
-        ) = self.get_factors(start=start, end=end)
+        ) = self.get_factors(start=start_frequency, end=end_frequency)
 
-        if x is None:
-            x = logspace(-10, 0, 1000)
+        for index in range(precision):
+            logger.debug(
+                _("search for a local minimum")
+            )
 
-        y = array(
-            [
-                sum(
-                    abs(
-                        Signal(
-                            factor_n.x,
-                            compute_light(
-                                pre_scatter_factor=x[i],
-                                factor_n=factor_n,
-                                coupling_n=coupling_n,
-                                factor_d=factor_d,
-                                coupling_d=coupling_d,
-                                phase=phase,
-                            ),
-                        )
-                        + reference
-                        - excited
-                    ).y
-                )
-                for i in range(len(x))
-            ]
-        )
+            x = logspace(log10(scatter_min), log10(scatter_max), 1000)
 
-        pre_scatter_factor: float = x[argmin(y)]
+            y = array(
+                [
+                    sum(
+                        abs(
+                            Signal(
+                                factor_n.x,
+                                compute_light(
+                                    pre_scatter_factor=x[i],
+                                    factor_n=factor_n,
+                                    coupling_n=coupling_n,
+                                    factor_d=factor_d,
+                                    coupling_d=coupling_d,
+                                    phase=phase,
+                                ),
+                            )
+                            + reference
+                            - excited
+                        ).y
+                    )
+                    for i in range(len(x))
+                ]
+            )
+
+            if argmin(y) == 0:
+                logger.warning(_("smaller than current range allows"))
+                scatter_max: float = x[1]
+            elif argmin(y) == len(x) - 1:
+                logger.warning(_("bigger than current range allows"))
+                scatter_min: float = x[-2]
+            else:
+                scatter_min: float = x[argmin(y) - 1]
+                scatter_max: float = x[argmin(y) + 1]
+
+        logger.debug(_("local minimum found"))
+
+        pre_scatter_factor: float = scatter_min / 2 + scatter_max / 2
 
         logger.info(
             _("found a scattering factor of {factor}").format(