We amend the general belief that waves with extended spherical wavefront focus at their center of curvature. Instead, when the spherical symmetry of waves is broken by propagating them through a finite aperture along an average direction, the forward/backward symmetry is broken and the focal volume shifts its center backward along that direction. The extent of this focal shift increases as smaller apertures are used, up to the point that the nominal focal plane is out of focus. Furthermore, the loss of axial symmetry with noncircular apertures causes distinct focal shifts in distinct axial planes, and the resulting astigmatism possibly degrades the axial focusing resolution. Using experiments and simulations, focal shift with noncircular apertures is described for classical and temporal focusing. The usefulness of these conclusions to improve imaging resolution is demonstrated in a high-resolution optical microscopy application, namely line-temporal focusing microscopy. These conclusions follow from fundamental symmetries of the wave geometry and matter for an increasing number of emerging optical techniques. This work offers a general framework and strategy to understand and improve virtually any wave-based application whose efficacy depends on optimal focusing and may be helpful when information is transmitted by waves in applications from electromagnetic communications, to biological and astronomical imaging, to lithography and even warfare.

我们修正了普遍的观点，即具有扩展的球形波前的波会集中在其曲率中心。相反，当通过沿平均方向在有限的孔径中传播使波的球形对称性破裂时，向前/向后对称性将被破坏，并且焦点体积将其中心沿该方向向后移动。当使用较小的光圈时，此焦点偏移的程度会增加，直至标称焦平面不在焦点上。此外，具有非圆形孔的轴向对称性的损失导致在不同的轴向平面中发生明显的焦点偏移，并且所产生的像散可能会降低轴向的聚焦分辨率。通过实验和仿真，描述了非圆形光圈的焦点偏移，用于经典和时间聚焦。这些结论对提高成像分辨率的有用性在高分辨率光学显微镜应用（即线时聚焦显微镜）中得到了证明。这些结论源于波几何的基本对称性和越来越多的新兴光学技术的重要性。这项工作提供了一个通用的框架和策略来理解和改善几乎任何基于波的应用，其功效取决于最佳聚焦，并且当信息在电磁通信，生物和天文成像，光刻甚至是波的应用中通过波传输信息时可能会有所帮助。战争。这些结论源于波几何的基本对称性和越来越多的新兴光学技术的重要性。这项工作提供了一个通用的框架和策略来理解和改善几乎任何基于波的应用，其功效取决于最佳聚焦，并且当信息在电磁通信，生物和天文成像，光刻甚至是波的应用中通过波传输信息时可能会有所帮助。战争。这些结论源于波几何的基本对称性和越来越多的新兴光学技术的重要性。这项工作提供了一个通用的框架和策略来理解和改善几乎任何基于波的应用，其功效取决于最佳聚焦，并且当信息在电磁通信，生物和天文成像，光刻甚至是波的应用中通过波传输信息时可能会有所帮助。战争。